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The main object of this book is to introduce, to such 
English readers as may be curious in the matter of music, 
the writings of the foremost musical theorist of Ancient 
Greece; and with this object in view I have endeavoured to 
supply a sound text and a clear translation of his great work, 
and to illustrate its more obscure passages by citations from 
other exponents of the same science. But further, since the 
mind of the modern reader is apt to be beset by prejudices 
in respect of this subject—some of which arise from his 
natural but false assumption that all music must follow the 
same laws that govern the only music that he knows, while 
others are due to the erroneous theories of specialists which 
have been accepted as certain truths by a public not in 
possession of the evidence—I have thought it necessary to 
deal at some length with those prejudices; and this is the 
chief aim of the Introduction. 

The critical apparatus differs from that of Marquard in 
including the readings of H as given by Westphal, and cor¬ 
recting from my own collation of the Selden MS. many 
incorrect reports of its readings. 

I wish to express my thanks to the Provost of Oriel 
College, Oxford, Mr. Mahaffy, and Mr. L. C. Purser, for 
reading the proofs, and for many useful suggestions; to 
Mr. Bury for advice on many difficult passages of the text; 
and above all to another Fellow of Trinity College, Dublin, 
Mr. Goligher, for most generous and valuable aid in the 
preparation of the English Translation. 

Trinity College, Dublin. 
Sept. 1902. 





A. —On the Development of Greek Music . i 

B. —On Aristoxenus and his Extant Works . 86 


book I 







book I 














A.— On the Development, of Greek Music. 

I. Music is in no sense a universal language. Like its 
sister, speech, it is determined in every case to a special 
form by the physical and mental character of the people 
among whom it has arisen, and the circumstances of their 
environment. The particular nature of music is no more 
disproved by the fact that a melody of Wagner speaks to 
German, French, and English ears alike, than is the particular 
nature of speech by the fact that the Latin tongue was at 
one time the recognized vehicle of cultivated thought 
throughout the civilized world. 

Further, this limitation which is common to music and 
speech leads to a more complete isolation in the case of 
the former. The primary function of language is to give 
us representations, whether of the facts of the world and 
the soul, or of the ideals of thought, or of the fancies of 
the imagination: and to appeal to our. emotions through 
the representation of such facts, ideals, or fancies. This 
service, so far as we are capable of perception and feeling, 
any strange language may be made to render us at the cost 
of some study. But we are aware that our own language 
has another power for us; that of waking immediately in us 
emotions in which are fused beyond all analysis the effects 
of its very sounds and the feelings that are linked to those 
sounds by indissoluble association. It is here that begins 
the real isolation of language, the incommunicable charm 
of poetry that defies translation. But the whole meaning 
of music depends upon this immediate appeal to our 
emotions through the association of feeling with sensation; 



and so the strangeness of the foreign music of to-day, and 
of the dead music of the past is insuperable, for they are the 
expressions of emotions which their possessors could not 
analyse, and we can never experience. 

2. The same contrast appears when we consider music 
in relation to painting and the other arts of imagery. These 
latter appeal to the emotions no less than music, but they 
do so in the first instance mediately, through the representa¬ 
tion of certain objects. It is quite true that here, as in the 
case of the emotions indirectly raised by language, the culti¬ 
vation of a certain mental habit is a necessary condition of 
our receiving the proper impression from any work of art. 
But in painting and sculpture the mental habit consists 
primarily in our attitude not to the manner of the repre¬ 
sentation but to the object represented, whereas in music it 
consists in our attitude towards the expression itself. 

The incommunicable character of music finds a striking 
illustration in the effect which the remnants of ancient Greek 
melody produce on the modern hearer. Some years ago, 
for example. Sir Robert Stewart delivered a lecture in 
Trinity College, Dublin, on the Music of Distant Times 
and Places; and illustrated it by specimens from various 
nationalities and periods, an ancient Greek hymn being 
included in the number. It was the unanimous verdict 
of all the musicians present that, while the music of the 
less civilized nations was often crude, barbarous, and 
monotonous in the highest degree, the Greek hymn stood 
quite alone in its absolute lack of meaning and its 
unredeemed ugliness; and much surprise was expressed 
that a nation which had delighted all succeeding genera¬ 
tions by its achievements in the other arts should have 
failed so completely in the art which it prized and practised 
most. Yet all this criticism is an absurdity based on the 
fallacy that music is a universal language. It presupposes 



absurdly that a melody is meaningless if it means nothing 
to us, and it forgets with equal absurdity that the beauty of 
an)rthing for us is conditioned by our power to appreciate it, 
and our power to appreciate it by our familiarity with it. 

3. But though it is impossible for us now to recover the 
meaning of this dead music of ancient Greece, and well-nigh 
impossible to accustom our ears to appreciate its form, we 
can at least study as a matter of speculative interest the laws 
of its accidence and syntax as they have been handed down 
to us by its grammarians. To this end our first step must 
be to make our conceptions clear as to the formal nature 
of music in general. We have already seen that the function 
of music is to evoke certain moods in us by the association 
of feelings with sensations. But the material of these 
sensations it does not find in nature, but provides for itself, 
by creating out of the chaos of infinite sounds a world of 
sound-relations, a system in which each member has its 
relation to every other determined through the common 
relation of all to a fixed centre. The idea of such a system 
implies two facts. In the first place, no sound is a musical 
sound except as perceived in its relation to another sound; 
in the second place, there is a direction in this relation in 
that one of the two related sounds must be perceived to be 
the inner, or nearer to the centre \ Thus in the chord 

or in the progression 

the sounds f and c become musical through their relation 
to one another, and through the perception in any particular 
case that one of them is more central than the other; in 
the key of C for example that the c, in the key of VB that 
the f is nearer the musical centre or tonic. 

^ Nearer, that is, in respect of similarity, not of contiguity. In 
this sense, the nearest note to any given note is its octave. 

« 2 



But just as the arithmetical intuition cannot apprehend all 
relations with equal ease, but finds for example the relation 
^ more intelligible than ; and as the sight apprehends 
the relation of a line to its perpendicular more readily than 
the relation between two lines at an angle of 87 degrees, 
so there stand out from among the infinite possible sound- 
relations a limited class, commonly called concords, which 
the ear grasps and recognizes without effort and immediately, 
and these form the elements of every musical system. Not 
indeed that all musical systems are founded on the same 
elementary relations. Universally recognized as belonging 
to this class are the relations between any sound and its 
octave above or below, either being regarded as tonic; the 
relation between a sound and its Fourth above, the latter 
being regarded as tonic; the relation between a note and 
its Fifth above, the former being regarded as tonic. But 
the relation of the Major Third which plays such a pro¬ 
minent part in modem music has no place as an elementary 
relation in the system of Ancient Greece. 

4. But evidently these few relations would go but a little 
way in the constitution of a system, and music to extend its 
sphere has recourse to the mediate perception of relations. 
Thus there are sound-relations, which the ear, unable to 
grasp them immediately, can apprehend by resolving them 
into the elementary concords. In our diatonic scale of c 
for example, the relation of to is resolved into the 
relation of d to g, and of g to c. Thus there enter into 
a musical system, besides the elementary concords, all those 
sound-relations which result from their composition; and 
to the complexity of such compound relations there seems 
to be no limit either in theory or in practice. There is no 
chord, no progression however complex, however unpleasant 
at first hearing, of which we can assert that it is musically 
impossible. The one thing needful to make it musical is 


that the relation of its parts to one another and to the 
preceding and succeeding sounds be comprehensible. 

It is also possible, though perhaps a sign of imperfect 
development, that a note may enter into a musical system 
through being related indeterminately to a member of that 
system. Thus we might admit a passing- note as leading 
to or from a fixed note, without the position of the former 
being exactly determined. 

Sound-relations can be perceived between simultaneous 
and successive sounds alike. In the former case we have 
harmony in the modern sense of the word, in the latter 
melody j the difference between these phases of music 
being accidental, not essential. 

The development of a system such as we have been 
considering will proceed upon-two lines. On the one hand 
the craving for diversity will lead to new combinations of 
relations, and so to the widening of the system and the 
multiplication of its members; while on the other hand 
the growing sense of unity will press for a closer determina¬ 
tion of the relations, and result in the banishment of those 
notes whose relations cannot be exactly determined. 

5. In the music of Ancient Greece we are able to trace, 
though unfortunately with some gaps, the first steps of such 
a development. The earliest students of the science, in 
endeavouring to establish a scale or system of related notes, 
started as was natural from the smallest interval, the bounding 
notes of which afforded an elementary relation. This they 
found in the interval of the Fourth, in which the higher note 
is tonic; and this melodic interval, essentially identical with 
our concord of the Fifth, may be r^arded as the funda¬ 
mental sound-relation of Greek music. When they had thus 
secured a definite interval on the indefinite line of pitch, their 
next concern was to ascertain at what points the voice might 
legitimately break its journey between the boundaries of this 



interval. But how were these points to be ascertained? 
Plainly, not by the exact determination of their relation to 
the bounding notes; for the Fourth was the smallest interval 
the relation of whose bounding notes the Greek ear could 
immediately apprehend; and for mediate perception the 
musical idea was as yet immature. Consequently, the in¬ 
termediate notes, whatever they might be, could only be 
apprehended as passing • notes, indeterminately related to 
the boundaries of the scale. Evidently then the number 
of such notes must be limited. The sense of unity which 
suffers by any inadequate determination of relations would 
be completely lost if the indeterminate relations were un¬ 
duly multiplied. From these considerations resulted one of 
the first laws of Greek melody. The scale that begins with 
any note, and ends with its Fourth above is at most a 
tetrachord or scale of four notes—two bounding or con¬ 
taining notes, two intermediate or contained. 

6 . Again; although for the theorist a minimum of musical 
interval is as absurd as a minimum of space or time, yet, 
for the purposes of art, it was impossible that any two of 
these four points of the scale should lie so close together 
that the voice could not produce, or the ear distinguish the 
interval between them. Was it then possible to determine 
for practical purposes the smallest musical interval? To 
this question the Greek theorists gave the unanimous reply, 
supporting it by a direct appeal to facts, that the voice can 
sing, and the ear perceive a quarter-tone^; but that any 
smaller interval lies beyond the power of ear and voice alike. 

Disregarding then the order of the intervals, and con¬ 
sidering only their magnitudes, we can see that one possible 
division of the tetrachord was into two quarter-tones and 

* The tone is musically (not mathematically) determined as the 
difference between the concord of the Fourth and the concord of 
the Fifth. These latter again are musically determined by the direct 
evidence of the ear. 



a ditone, or space of two tones; the employment of these 
intervals characterized a scale as of the Enharmonic genus. 

Or again, employing larger intervals one might divide the 
tetrachord into, say, two-thirds of a tone, and the space of 
a tone and five-sixths : or into two semitones, and the space 
of a tone and a half. The employment of these divisions 
or any lying between them marked a scale as Chromatic, 
Or finally, by the employment of two tones one might 
proceed to the familiar Diatonic genus, which divided the 
tetrachord into two tones and a semitone. 

Much wonder and admiration has been wasted on the 
Enharmonic scale by persons who have missed the true 
reason for the disappearance of the quarter-tone from our 
modem musical system. Its disappearance is due not to 
the dullness or coarseness of modern ear or voice, but to the 
fact that the more highly developed unity of our system 
demands the accurate determination of all sound-relations 
by direct or indirect resolution into concords; and such 
a determination of quarter-tones is manifestly impossible ^ 

7. But the constitution of our tetrachord scale is not yet 
completed. We have ascertained the maximum number 
and the various possible magnitudes of the intervals; but 
their order has yet to be determined. In the Enharmonic 
genus, for example, when we are passing to the tonic from 
the Fourth below, shall we sing quarter-tone, quarter-tone, 
ditone; or ditone, quarter-tone, quarter-tone; or quarter-tone, 
ditone, quarter-tone; or are all these progressions equally 
legitimate? To these questions the Greek theorists give 
the unqualified and unanimous answer, not defending it by 
any argument, that in all divisions of a tetrachord in which 
the highest note is tonic, and the lowest a Fourth below, the 
lowest interval must be less than or equal to the middle, 
and less than the highest. 

’ See below, note on p. 115, 1 . 3. 



Thus the schemes of the tetrachord scales inthethree genera 
are finally determined as they appear in the following table:— 








In this table the following points are to be noted:— 

(1) The sign x is used to signify that the note before 
which it is placed is sharpened a quarter-tone. 

(2) The distinction between the definitely determined 
bounding notes, and the indeterminate passing notes is 
brought out by exhibiting the former as minims, the latter 
as crotchets. 

(3) Several divisions are possible in the Chromatic and 
Diatonic genera (see below, p. 116): those taken in this 
table are merely typical. 

8. The importance of this tetrachord scale can hardly be 
overrated, for it is the original unit from the multiplication 
of which in various positions arose all the later Greek 
scales : and it is to be observed that the tonality of this 
scale is most distinctly conceived and enunciated by the 
theorists. Aristoxenus is never weary of reminding us that 
the mere perception of intervals cannot enable us to under- 


stand a succession of notes; that we must also apprehend 
the Svvaftts or function of each individual in the series. 
Thus the highest note of the tetrachord, which at a later 
period when the scale was enlarged, obtained from its 
position the name of Mese, or middle note, holds in relation 
to the lowest note the function of an apx^ or foundation, in 
other words of a tonic. For just as cause and effect, though 
they exist only in their relation to one another, do not 
discharge like functions in that relation inasmuch as the 
effect leans upon the cause, but not the cause upon the 
effect; so though the highest and lowest notes of the tetra¬ 
chord are musical notes only through their relation to one 
another, yet that relation is conceived as implying the 
dependence of the lower upon the higher, but not of the 
higher upon the lower. The intermediate notes again are 
regarded as mere stopping places of approximately deter¬ 
mined position in the passage between the boundaries. 
According to the Greek terminology they are Kivoipevot or 
movable notes as distinguished from the iarSyres or fixed 
notes, between which they stand. For since the essence 
of a note is not its place in a group, but its function in 
a system, an Enharmonic, a Chromatic, and a Diatonic 
passing note are not to be regarded as three notes, but as 
one variable note in three positions. 

Even if we disregard the Enharmonic and Chromatic 
genera, and confine our attention to the Diatonic, we shall 
seek in vain for a parallel to this tetrachord scale in the 
classical system of modern music. We can descend from 
the tonic a to the e below it by the progression 

to the tonic a, though of frequent occurrence in local music, 
has passed completely out of classical use. 


but the progression 



9. When this meagre group of four notes was felt to be 
inadequate to the expression of human emotion, a ready 
method for the production of a more ample scale was 
sought in the addition to the original tetrachord of a second 
exactly similar to it. But immediately the question arose, 
How was the position of the second tetrachord to be deter¬ 
mined in relation to the first ? Or, to put it more generally. 
Supposing a scale of indefinite length to be constituted by 
a series of similar tetrachords, how was the position of these 
tetrachords to be relatively defined ? 

To this question it seems that there were three possible 
answers for the theorist, each of which no doubt found 
support in the art product of some tribe or other of the 
Hellenic world. The method of determination proposed 
in each answer constituted (as I shall here assume, post¬ 
poning my arguments for the present) a distinct SpuovU or 
Harmony ^; which term I believe to have meant primarily 
an ‘ adjustment ’ not of notes (for these are not the units of 
music) but of tetrachords. 

10. According to the first of these answers, the tetra¬ 
chords might be so arranged that the highest note of any 
one would coincide with the lowest note of the next above 
it. This method of conjunction^ or the coincidence of 
extremities I believe to have been called the Ionic Har¬ 
mony ; and it resulted in a scale of this character:— 




Enharmonic I 

^ When I use the word Harmony as an equivalent of the Greek 
dpfxovia, 1 shall employ a capital H. 




If in the Ionic scale of any genus we take any con¬ 
secutive pair of tetrachords, we obtain the Heptachord scale 
of the seven-stringed lyre. 

TABLE 3 . 


II. These names were derived not from the pitch of the 



respective notes, but from the place on the instrument of 
the strings which sounded them. Thus a as the note 
of the middle string was called Mese or ‘ middle ’; e was 
called Hypate or highest because sounded by the top string; 
d which was sounded by the bottom string was in like 
manner called Nete or lowest. The note below the Mese 
was called Lichanus or ‘forefinger,’ because the string 
that sounded it was played by that finger. The names 
Parhypate, ‘next the highest,’ Paranete, ‘next the lowest,’ 
and Trite, ‘third,’ require no explanation. 

It is important to observe exactly what these names do, 
and do not denote. They do not denote the members 
of a scale as points of pitch determined absolutely or in 
relation to any other scale. Let us take the scale 

and transpose it, say, a tone higher 










the individual notes of the resulting scale will bear the 
same names as the corresponding members of the original 

Again, these names do denote the points of a scale the 
order of whose intervals is determined. Thus, if we take 
the enharmonic scale 



consisting not of two complete tetrachords, but of one 
tetrachord and a fragment at each end, the notes of these 
scales will take their names from their place not in their own 
scales, but in the typical systems given in Table 3 , 

Once again, it is not implied by these names that the 
intervals between the designated notes are exactly deter¬ 
mined in magnitude; for they are applied to the members 
of Enharmonic, Chromatic, and Diatonic scales alike. 

1 2. The second method of forming a scale of tetrachords 
left the interval of a tone, called the disjunctive tone, be¬ 
tween each pair of them. This Harmony by disjunction, or 
the separation of extremities, I shall assume to have been 
called Doric. It substituted for the Heptachord the Octa¬ 
chord, or scale of the eight-stringed lyre. 

TABLE 4 . 




The scale of this Harmony, when indefinitely prolonged, 
resulted in the following succession :— 

TABLE 5 . 


The appearance of the octachord scale necessitated an 
alteration in the nomenclature. The old names were em¬ 
ployed to represent the four lowest and the three highest 



members of the new system, and the title Paramese, or 
‘ next the middle,’ was given to the note above the Mese. 

13. The third method of adjustment employing conjunc¬ 
tion and disjunction alternately interposed a tone between 
every second pair of tetrachords, while every other pair 
were conjunct. This Harmony I shall assume to have been 
called Aeolian; it resulted in the following scales :— 










~ y — 

— 1 — 1 -^ 

.1 jtj 


- 1 — 

—1—1 —1 

1 1 j j 



The alternation of conjunction and disjunction which is 
the characteristic of this Harmony is exemplified in the 
following eight-note scales:— 

TABLE 7 . 






14. If we employ modern nomenclature we may distin¬ 
guish the first two Harmonies from the last by saying 
that the former give rise to modulating scales, the one 
passing over into the flat, the other into the sharp keys, 
while the latter maintains the same key throughout. But 
we must examine more closely into the nature of this 
difference. In the scale of the first Harmony we have a 
series of lesser tonics £, A, d, ; that is, each of these 
notes serves as tonic to the notes that immediately precede 
it. What then is the relation of these tonics to one an¬ 
other ? Each serves as a tonic of higher rank to the lesser 
tonic immediately below it and mediately through this to 
all below, so that we are necessarily driven upwards in our 
search for the supreme tonic, and are unable at any point 
to reverse the process; for no note can serve as immediate 
tonic to the Fourth above it. Consequently our progress 
towards the supreme or absolute tonic becomes a process 
ad infinitum. 

When we pass to the second Harmony we find an opposite 
condition of things. Here the series of lesser tonics is 
D, A, e, b. Any one of these serves as tonic of higher 
rank immediately to the lesser tonic next above it, and 
through this mediately to all above, but cannot discharge 
a like function to those that are below it. Here then the 
necessary order is the descending one, but the progression 

^ When any scale contains the same note in two different octaves, 
we shall represent the higher by small, the lower by capital letters. 


is equally ad infinitum ; and our search for an absolute tonic 
is again fruitless. But when we arrive at the third Harmony 
we find for the first time the object of our search. In the 
series E, A, e, a, A is tonic to the e above through the 
mediation of a \ and directly to the E below, and through 
them to all the lesser tonics of the scale. 

15. The distinction, then, that holds between these three 
Harmonies corresponds in no wise to the distinction between 
our Major and Minor modes. All three of them alike recog¬ 
nize no fundamental relations outside that of a note to its 
Fourth above or Fifth below, and that of a note to its octave; 
and all three alike place their passing notes in the same 
position. But our distinction of Major and Minor has 

arisen through the recognition of two fresh elementary 


sound-relations unknown to the Greeks, those of the 

Greater and Lesser Third; and according as a scale 


embodies one or other of them, it is denominated Major 
or Minor. Thus the essential characteristic of the major 
scale of A is the immediate relation of f C to A, and of f 6^ 
to E; and of the minor scale of A, in so far as we have 
a minor scale at all, the immediate relation of C to A, and 
of 6^ ta ^; and these relations are not present in the scales 
of any of the three Harmonies. One might illustrate the 
contrast by representing the modern minor scale of A as 

* The relation of a note to its octave above or below approximates 
to identity. 




and the diatonic scale of the third Harmony as follows :— 

in each case supplying the most fundamental relations of 
the scale in the form of a bass. 

16. From the comparison above instituted between the 
three early Harmonies of Greek music, it was clear that 
the third possessed a consistency and unity which were 
wanting in its rivals. Accordingly we are not surprised to 
find that they fell into disuse, while the Aeolian won its 
way to predominance, and finally to exclusive possession 
of the field of melody. But the process was a gradual 
one, and there were many attempts at combination and 
compromise before it was accomplished. Of such attempts 
we have an example in the so-called Phrygian scale, the 
earliest form of which is given us by Aristides Quintilianus 
(Meibom, 21. 19). 




Here we have a scale which, though containing two dis¬ 
junctions (between D and E, and between A and B\ yet 
produces an octave by combining conjunction with dis¬ 
junction at A, and in so doing embodies the distinctive 


feature of the first Harmony, the relation of the tonic A to 
d, its Fourth above. 

17. The perverse artificiality which is conspicuous in this 
scale is a common feature in the musical science of the 
period. It does not by any means follow that the music 
of the time suffered from the same vice. For the sake 
of brevity, we have regarded the theorists as gradually 
evolving the system of Greek music; but of course their 
province as a matter of fact extended only to the analysis 
and explanation of what the artist created. As the theorist 
of metrical science arranges in feet the rhythm to which 
the instinct of the poet has given birth, so the theorist of 
scales offers an analysis of the series of notes in which the 
passion of the singer has found expression. Now, the art 
which in the beginning had created the tetrachord and then 
passed on to the various combinations of tetrachords came 
to require for some song or chorus the following diatonic 
series of notes:— 



This scale the theorist applied himself to read, and the 
scheme of Table 8 is the fruit of his first attempt. When 
the distracting claims of the First and Second Harmonies 
had become silent, and the Third had come to be recog¬ 
nized as the normal method of combining tetrachords, the 
true reading of the scale became apparent 

18. Aristides Quintilianus has preserved for us several 
other examples of these perverse scale-readings. Composers 
found room for variety within the Aeolian Harmony by 
employing now one, now another segment of the indefinite 

c 2 19 


Aeolian scale, not of course with any change of tonality or 
modality, but simply as the melody required this or that 
number of notes above or below the tonic. Thus there 
arose a series of scales which offered material for the analysis 
of the theorist—an analysis that was not by any means so 
easy and obvious as we might at first suppose. We seem 
immediately to recognize that they are not essentially in-* 
dependent of one another, but differ merely as various 
portions of one scale; and we are disposed to wonder that 
the Greeks should have deemed each of them worthy of 
a separate analysis and a name to itself. But there are two 
important considerations which are apt to escape us. In 
the first place, at the period of musical science which we 
are now considwing, the contending claims of the three 
Harmonies, and the possibility of combining them produced 
an uncertainty in the analysis of scales, of which music, 
through the simplifying tendency ever present in its develop¬ 
ment, has since cleared itself. In the second place, we are 
accustomed to instruments of great actual or potential 
compass, in which the relation of such scales to one another 
as segments of a common whole is immediately and palpably 
evident. But for any performer on a limited instrument, 
say, one of eight notes, it would be impossible to pass from 
one of these scales to another except by a fresh tuning, or 
in some cases by a change of instrument; and from these 
practical necessities the scales would derive a character of 
independence which does not belong to them in the nature 
of things. We should never think of differentiating and 
distinguishing by name the octave scales in which are 
respectively contained the opening phrases of Handel’s 
‘ I know that my Redeemer liveth,’ and his ‘ But thou did’st 
not leave his soul in hell.’ But it would be natural enough 
for a player on the pipe to do so when he found that the 

two themes could not be rendered by the same instrument. 



19. Again, these scales that had to be analysed were in 
common vogue, and so belonged to the Diatonic Genus. 
For here it is to be observed that the Enharmonic and 
Chromatic scales seem to have been esoteric or academical 
in use, and the pre-eminently natural character of the 
Diatonic was recognized even by those theorists who 
defended the other genera (see below, p. ri i', 1 '. 9). We 
append a table of the scales to be analysed. 

TABLE 9 . 







It is most carefully to be noted that, in order to conceive 
of these scales as did the Greeks, we must entirely abstract 
from the pitch relation which is necessarily introduced into 
them by representing them according to modem notation. 
Any one of the above scales may lie higher, or lower than, 
or in the same compass as any other of them. 

20. To guide them in their analysis the theorists were 
not without certain clues. No note, they knew, could be 
the tonic or Mese of the scale unless the fourth note below 
it stood to it in the fundamental relation of a note to its 
Fourth above. And the increasing influence of the Third 
Harmony made it necessary to find the tonic in a note 
next above which lay the disjunctive tone. But even with 
these clues the scales often baffled their analysis. Authori¬ 
ties differed, and in one case at least a historian* records 
the discovery in later times of the true reading of a scale 
which had formerly been misinterpreted. Nothing, perhaps, 
contributed more to these doubts and failures than the 
endeavour to find a distinctive plan of formation in each 
scale. In accordance with this principle (d) in the above 
table was construed as two complete tetrachords of the 
Dorian Harmony, and was augmented by a tone so as to 
represent adequately the nature of that adjustment by dis- 

* See Plutarch, de Musica, 1136 d Aiats di Aajxnpoic\ia rbv'AOijvcuov 
ffvyiSovra ort oiit ivravda lx*‘ MifoAvStffri) Sia^tv^iv, otrov <rx*83i' 
avavrtt ^ovto, dX\’ lirl ri 1;, toiovtov ainfjs intpyaaaffOat t6 axfjixa olov 
rb dvb vapafiifftjs iirl ivarTjy inarwy. ‘ But according to Lysis Lampro- 
cles the Athenian saw that the Mixolydian scale had its point of dis¬ 
junction, not where it was commonly supposed to be, but at the top ; 
and accordingly established its figure to be such a series of notes as 
from the Paramese to the Hypate-Hypatdn.’ 



junction only. According as this tone was added at the 
bottom or at the top, the scale would seem to have been 
called Dorian or Hypodorian (that is, Lower Dorian). The 
appropriateness of this latter name will appear in the 

TABLE 10 . 



The reading of {c) resulted in the Phrygian scale, the 
scheme which we gave in Table 8; (^) and {e) were iden¬ 
tified as illustrating alternate conjunction and disjunction, 
and, as typical of the Aeolian Harmony, were called Lydian’. 

TABLE 11 . 


Again, (/) was read as in the following table, and, as 
essentially similar to the Phrygian scale, was called Hypo- 

^ For the relation between the terms Aeolian and Lydian see 



TABLE 12 . 




{g) does not appear in the oldest lists of scales. Perhaps 
the extreme position of the tonic made such a segment of 
rare occurrence. The same fact may have helped to obscure 
the analysis of {a). Certain it is at any rate that not only 
the true plan, but even the position of the tonic of this 
scale remained for a long time undiscovered (see note 
on p. 22). Aristides Quintilianus (Meibom, 21. 26) has 
preserved for us the old reading which is curiously in¬ 

TABLE 13 . 



-p- Tfr 

I V_L_ 







We have already seen that the term Lydian was applied 
to the scale that was typical of the Aeolian Harmony; and 
consistently with this, {a), as a mixture of two such scales, 
was called Mixolydian or Mixed Lydian. It was an example 
of what Aristoxenus calls a double scale; that is, it had 
two Mesae or tonics, d and e. 

21. Each of these scales might, at any rate theoretically, 
appear in Enharmonic and Chromatic as well as in Diatonic 
form. The following is a complete table of them in every 

TABLE 14 . 


{d) Mixolydian. 


{b) Lydian. 


I I 






(<r) Phrygian. 



{d) Dorian. 





It is to be noted that in the Enharmonic and Chromatic 
scales it often appears that more notes occur than in the 
corresponding Diatonic. The reason is this. If a diatonic 
scale exhibits, say, the combination of the conjunction e-a 
along with the disjunction e-^f-b, the fixed note a of the 
conjunction will coincide in pitch * with the second passing 
note a of the disjunct tetrachord 4 ^ a, b and so will 
not be a different note from it according to our notation. 
But in the corresponding Enharmonic and Chromatic scales 
there will not be such a coincidence, and consequently our 
notation is able to distinguish such notes in these genera. 

22. As soon as the formal essence of these scales had 
been established we find the Greek theorists exercised with 
the question of their proper keys, in other words of their 
pitch. At first sight the question seems an absurd one. 
In the nature of things no scale, regarded as a mere order 

^ Not in function. 



of intervals can be determined to any particular pitch; and 
though practical necessities reduce the possible pitch of all 
scales within certain limits, they do not define the relative 
position of different scales within those limits. Let us take 
for example the Lydian and Phrygian scales; and, that our 
conceptions of them may be wholly free from any admixture 
of pitch relation suggested by our modern notation, let us 
assume as scheme of the Lydian:— 

and of the Phrygian :— 

tone ^ tone tone tone tone i tone tone 


If then we suppose the limit of practically possible sounds 
to be two octaves, from 

one might take as Lydian scale 

in which case the Lydian is higher than the Phrygian : or 
again, one might take as Lydian 



and as Phrygian 

in which case the Phrygian is higher than the Lydian: or 
again, one might take as Lydian 

and as Phrygian 

in which case the scales coincide in pitch. 

23. An explanation of the question that would naturally 
suggest itself to any modern reader is that the Greek theorists 
desired to reduce these scales to segments of one universal 
scale, and establish thereby a theoretical relation of pitch 
between them; just as we, finding types of most of the 
scales of Table 14 inside the series of the white notes of 
a piano, theoretically regard (c) for example as a tone above 
(d). But this explanation is immediately confronted by two 
objections, each of which is fatal to it. In the first place, 
the Greek theorists attributed to each scale in virtue of its 
formal essence an absolute ethical character, and they con¬ 
ceived that character as dependent on its pitch. Its pitch, 
then, must have been something more than a mere theo¬ 
retical relation. And in the second place the answer 
actually given to the question is precisely the reverse of 
what it must have been if the above explanation of the 
question were true. For the Greek theorists state that the 
Phrygian scale whose scheme is (^r) in Table 14 is one tone 
not above but below the Lydian, whose scheme is (6). 

We must conceive, then, this question of the pitch of the 
scales as implying the possibility of determining each of 



them to a particular pitch, not arbitrary, but arising ne¬ 
cessarily from the order of its intervals; not theoretical, or 
relative, but serving as the ground of an absolute ethical 
character ; not leading to such an order of the scales as 
would arise from the reduction of them to segments of one 
series, but to precisely the reverse order. 

24. To understand the possibility of such a determination 
we must take into account an important distinction between 
ancient Greek melody, and the melody of modern music. 
We have seen that the essential feature of music is the 
relation of all the notes of a scale or system to its central 
point or tonic. To maintain the sense of this relation, it is 
necessary in every musical composition, that the tonic should 
be expressed with due frequency; and all the more neces¬ 
sary when the musical consciousness is immature. Modern 
music indeed can fulfil this requirement by means of har¬ 
mony ; and so it is not unusual to have a melody of any 
length in which the tonic seldom or never occurs. But the 
music of Ancient Greece, lacking the assistance of harmony, 
could not thus dispense with its tonic; and accordingly 
we find Aristotle * enunciating the law that melody should 
constantly recur to the Mese, as to the connecting note 
from which the scale derives its unity. Now, let us suppose 
a singer, boy or man, or a performer on lyre or flute to 
have at his disposal only eight serviceable notes; and let us 
imagine him to sing or play a melody in the Lydian scale. 
Here the Mese is third note from the top, and sixth note 
from the bottom. Consequently it lies in the higher part of 
his register, or among the higher notes of his instrument; 
and the melody necessarily gathering itself around this note, 
and constantly repeating it, will assume a high-pitched tone. 
But now let us imagine him to pass to a melody in the 
Hypophrygian scale. Here the Mese is second note from 

' Problems^ xix. ao. 



the bottom, and seventh from the top. Therefore it lies in 
the under part of his register or among the lower notes of 
his instrument; and the melody gravitating towards this 
note necessarily assumes a low-pitched character. Thus 
the pitch of a Greek scale is determined not by the absolute 
position of its tonic, nor by the pitch relation between its 
tonic and the tonic of any other scale, but by the position 
of its tonic in relation to its other notes. When for example, 
it is asserted that the Lydian scale is a tone higher than the 
Phrygian, the meaning is that, while the Phrygian tonic lies 
two and a half tones from the top, and three and a half 
tones from the bottom of the Phrygian scale, the Lydian 
tonic lies one and a half tones from the top, and four and 
a half tones from the bottom of the Lydian scale. Thus it 
is seen that the relative determination of the pitch of these 
scales is only made possible by the fact that each has an 
intrinsic pitch character of its own, consisting in a pitch 
relation between its own members. 

25. The relative pitch of the six scales of Table 14 may 
be presented to the eye by placing them as in the following 
table between the same limiting notes, except that the Dorian 
and Hypodorian will extend a tone lower inasmuch as they 
exceed the others by a tone. 

TABLE 15 . 









Mixolydian _ . 

Tonic Tonic 

* :(( 

Dorian ^ . 







I have omitted the Enharmonic and Chromatic scales in 
this table, as the Diatonic are sufficient to illustrate the 
principle before us. 

If we assume the pitch of the Mixolydian tonic to be f (r 
which lies intermediate between the two Mesae G and A; 
the tonics of these scales taken in the above order are f 
G, f G, A, B, f C. We naturally conclude that the lowest 
scale is the Hypophrygian, and the Hypodorian, Mixolydian, 
Dorian, Phrygian and Lydian follow it at intervals re¬ 
spectively of a semitone, a semitone, a semitone, a tone, 
a tone, a tone. When at a later time the true construction 
of the Mixolydian was discovered, and its Mese was seen to 
be D, its position in the pitch series was changed, and it 
became the highest of the scales. (See below, p. 128.) 

26. Besides these scales, all of which are complete or 
continuous in the sense that they employ all the notes 
melodically possible between their extremities, Greek art 
made use at this time of certain deficient scales which 
were called transilient, because they skipped some of the 
possible stopping places in their progression. The following 



transilient scales in the Enharmonic genus are recorded 
by Aristides Quintilianus (Meibom, p. 21). 

(a) Ionian 

(b) High Lydian 


The Ionian scale of Aristides Quintilianus would seem to 
have been obtained from the scale of two conjunct tetra- 
chords by the omission of the two passing notes of the 
upper tetrachord, and the introduction of one of the passing 
notes of the disjunct tetrachord 

It is thus an example at the same time of deficiency and of 
the mixture of conjunction and disjunction ; and the compari¬ 
son of it with the Phrygian scale supports us in our view that 
the characteristic feature of Phrygian and Ionian music alike 
was the retention of the Fourth above the tonic. 

27. From this point the development of the Greek musical 
system proceeded upon lines which are easy to trace. The 
most prominent moments in that development were the 
growing importance of the Diatonic genus in comparison 
with the Enharmonic and Chromatic, and the disappearance 
of the Dorian and Ionian Harmonies. Thus the develop¬ 
ment was a process of simplification in which the artificial 
scale-readings which we have been considering were gradually 
eliminated. It was seen that the section of the diatonic 
scale of the Aeolian Harmony from D to d (see Table 9) 
contains all the same characteristic features as the so-called 
Phrygian scale in the same genus. Similarly the Hypophry- 
gian scale was seen to be the segment from G tog. Similarly, 
as we have already said, the Mixolydian scale was seen to 
be that portion in which the Mese stands second note from 
the top. The Dorian and Hypodorian scales were deprived 
of the second disjunctive tone which was their distinctive 
feature, and were merged by coincidence in the one scale 
called Dorian which was the segment between £ and e. 
Thus finally all distinctions of Harmonies perished ; hence¬ 
forth all scales were but the rponoi or modes of one note- 


series. To complete the number, the modes from F to f 
and from A to a were called respectively Hypolydian and 
Hypodorian on the analogy of the Hypophrygian. The 
results of this process of simplification are given in the 
following table:— 

TABLE 16. 





- Xi 











gj. x < 





D 2 











The pitch relations of the seven modes are exhibited in 
the next Table. 

TABLE 17. 







Tonic I I 





Tonic • I 

1—^ J 




Tonic . I 

gg ,-j w =g 



J - 


2 ± 





j = i ’4 







From this table it appears that the Hypodprian with its 
tonic i^is the lowest of the modes, and the Hypophrygian, 
Hypolydian, Dorian, Phrygian, Lydian, and Mixolydian 
follow at intervals respectively of a tone, a tone, a semitone, 
a tone, a tone, a semitone. 

28. At the risk of falling into vain repetition, let us again 
consider the essence of the distinction between these modes. 
It is not a distinction of modality such as exists between 
our major and minor scales. The development of Greek 
Music preserved, amidst all its changes, the original tetra- 
chord as the permanent unit of composition. And even 
the differences that came into being through the various 
Harmonies had not survived, so that the principle of con¬ 
struction remained identical in the change of mode. 



Again, it is a distinction in the order of intervals, but only 
in so far as the several modes are different sections of one 
common whole. 

Again, it is a distinction of pitch, but not such as exists 
between our keys, for it arises immediately from the order 
of intervals. The Mixolydian is a high mode because any 
melody composed in it, whatever be the absolute pitch of 
its total compass, must necessarily lie for the most part in 
the upper region of that compass. 

Finally, because it is such a distinction of pitch, it is also 
a distinction of ethos or mood. To understand this, let us 
assume that high tension of the voice is the natural expres¬ 
sion of poignant grief, an easy relaxation of it the natural 
expression of sentimentalism; let us suppose, too, that to 
represent these emotions respectively a musician desires to 
write two songs, neither of which is to exceed the compass 
of an octave. How, then, shall he bestow the required 
character on each of these melodies? Evidently not by 
choosing a low key for one and a high key for the other, in 
the modern sense of the terms ‘ high ’ and ‘ low ’ key; for 
this would imply that all first treble songs must be tragic, 
and all bass songs sentimental. He must, instead, leave 
the general pitch of the songs undetermined, so that either 
of them may suit any voice; but he must so compose them 
that the one will lie chiefly in the upper, the other in the 
lower region of the undetermined eight-note compass. And 
this a Greek musician could only effect by choosing, for his 
pathetic song, a scale in which the tonic lay near its upper 
extremity, and for his sentimental, one in which its position 
was the reverse 

^ Cp. Ptolemaeus, lib. ii, cap. 7 ov5k ydp ^vticev rSiv fiapvripojv ij 
o^vripov (patvSiv ivpoifitv hv rip> avaraffiv rrjs Kara rbv tovov pLtTafioXfji 
y€y(V7fpivT)V, oitirt vpbs Ti/v rouvuTtfV Sicupopdi' 17 ruy opyAvwv S\cjy 
imraffts ^ iraXiv iveats dnapicft, /MjSc/uas ye vapaXXayiji vepl rb fie\os 



29. At this stage the compass of the Greek scale, whose 
growth from tetrachord to heptachord, and from hepta¬ 
chord to octachord we have already witnessed, underwent 
a further extension. To the typical scale 




















4 >» 






4 -» 



-i-d- H - 



J _G 

^ - & 

were added at its upper extremity a conjunct tetrachord 

and at its lower extremity a conjunct tetrachord and an 
additional note below (called the irpoaXafi/iavofieyos) at the' 
interval of a tone 

The resulting scale was called the Greater Complete System. 

dnoT€\ovfJLivr]Sy orav o\ov o/xoiojs vnb tS>v Papv<pa)VOTipojv ^ rwv o(v<p<tivo^ 
rkpoiv dyojviGTWv diaiicpaivrjTai' dW* %v€Ka rod /card rfjv piav ipojvfjv rd 
avTo ttotI fiiv and ran/ b^vripoov rdnojv dpxbjx^vovy irori SJ dirb 

tS)v PapvTipoJv, rpoirrjv riva rov ^$ovs dnoreXciv, *Nor should we find 
that modulation of key was introduced for the sake of higher or lower 
voices ; for this difference can be met by the raising or lowering of the 
whole instrument, as the melody remains unaffected whether it is 
performed consistently throughout by artists with high or by artists 
with low voices. The object of modulation is rather that the one 
unbroken melody sung by the one voice may produce a change of 
feeling by having its tonic (lit. ‘having its beginning’) now in the 
higher, now in the lower, regions of that one voice.’ 



As will be seen from this table, all the notes of the Greater 
Complete System with the exception of the Proslambano- 
menos were distinguished by the same names which had 
been employed for the eight-note scale with the addition of 
a term to mark the particular tetrachord to which each 
belongs. The tetrachords were named in order Hypaton i.e. 
‘of the lowest VMesdn i.e.‘of the middle,’ Diezeugmenon® i.e. 
‘ of the disjunct,’ Hyperbolaeon i.e. ‘ of the highest ’ notes. 

Side by side with the Greater Complete System there 
stood another scale called the Lesser Complete System, in 
which was preserved the tradition of the Ionian Harmony 
and the heptachord scale. The following table exhibits its 
scheme and nomenclature:— 

TABLE 19. 


Hypat6n Mes6n Synemmen6n 

^ Literally ‘ of the highest.’ The highest or top string of the lyre 
gave the lowest note. ^ Also called Neton. 



30. The following table exhibits the seven modes with 
the names of their notes according to the nomenclature of 
Table 18 

TABLE 20. 

































. c 


V? c 
Q V 

•n 3 
^ 0) 







C -w 

Cd cd 

JS cu 









M • 






































4 >» 





U 4 



c 3 


P 4 




Mes6n Diezeugmen6n 





a s 




























H o, 

The nature of each mode as merely a segment of the 
typical scale of Table i8 is here apparent; and the theorists 
showed their full recognition of this fact by extending, as is 
done in the following table, each of the modes to the typical 
compass of two octaves. The result is a series of seven 
scales identical in figure or order of intervals, but deter- 
minately distinguished from one another by the relation of 
their pitch. In other words, the modes or rpoiroi have 
become tovoi or keys. 



TABLE 21. 


The modes are marked off by bars. 

Mixolydian _ Q 

This is a very striking change of conception. It means 
that the sense of the independent and distinct character of 
the modes was almost extinct. But this was an inevitable 
consequence of musical development; for that sense pre¬ 
supposed the limitation of the scale to an octave, and this 


limitation necessarily vanished before the widening demands 
of a growing art, and the larger possibilities of more elaborate 

31. The number of the keys was afterwards, apparently 
by Aristoxenus, raised to thirteen by the addition of 
(i) a key at a semitone below the Phrygian, called the 
Second Phrygian or Ionian; (2) a key at a semitone below 
the Lydian, called the Second Lydian or Aeolian; (3) a key 
at a semitone below the Hypophrygian, called the Second 
Hypophrygian or Hypoionian; (4) a key at a semitone below 
the Hypolydian, called the Second Hypolydian or Hypo- 
aeolian; (5) a key at a semitone above the Mixolydian, called 
the Hyperionian; (6) a key at a semitone above the Hyper- 
ionian, called the Hyperphrygian. In this scheme the 
Mixolydian key took the name of Hyperdorian on the 
analogy of Hyperionian and Hyperphrygian. At a still 
later date two higher keys were added at intervals of a semi¬ 
tone and tone above the Hyperphrygian, and were called 
respectively the Hyperaeolian and Hyperlydian. Thus we 
obtain the full number of fifteen keys which we find with 
their notation in the fragment of Alypius. 

In the following table for the sake of completeness and 
convenience of reference, we present these fifteen keys with 
their notation*, and in the three Genera, including the 
tetrachord Synemmenon of the Lesser Complete System. 

* On the question of the Greek notation, the reader is referred to 
Westphal, Harmonik und Melopoie der Griechen (c. viii) ; Gevaert, 
Musique de VAntiquUe (t. I. pp. 244 flf) ; Monro, Modes of Ancient 
Greek Music (§ 27). Each sound was denoted by two characters, 
one for the voice, and one for instruments. The vocal characters are 
plainly derived from the ordinary alphabet; but both the forms and 
the order of the instrumental characters raise great difficulties. 




TABLE 22 . 


S (A 

"I C 
- i 

O o 
c a 
0 ^ 




p n 

u D 

0 H 
V > 

p n 

u D 


0 H 
V > 




P M 

u n 

0 r 

V N 

T c n K 

1 C D A 

T C n K 

=! C 0 A 

T C O K 

=1 C K A 

I Z 
< C 

NC {L.| NCJ ^4 NCJ 


TABLE 22. 

Synemmenon Diezeuginen6n Hyperbolaeon 

<6 ^ M' e A X r 0' H' u' 
X A n' A. \ <’ S' >' T 

A ^ M' e A X r 0' H' u' 

A A n' '1 /■ \ <’ S'>' T 

A X M' e A M' r 0' r u' 

A \ H' '1 n' <' V' N' T 

U ^ O' !F 0 X K' I' H' A' 
Z X K' X M \ K <’>' y 

U ^ O' ^ 0 X K' I' H' A' 
Z X K' X '1 \ A' <'>' \' 

U 0 O' IF 0 O' K' I' Z' A' 
Z 'I K' X 'I K' A' <' C V 







*3 <n 

^ I 
O I 

^ C 

Enharmonic ^ 



4) r T 





n(t)YTM AKr 

A Fu-TT ^AN 



^ -<s»- 

r n M 
u- D n 

A H r 

-< > N 



X (f) T 

^ F =1 

H N 
^ >1 


X <|) T o = N Z 

H F 1 K ^ >1 C 



X <t) C O H I Z 
‘V F C K < C 



Synemmendn Diezeug^endn Hyperbolae6n 

E A e A U ^ O' H' N' Z' 

U 1 M \ Z X K' >1' C' 

E A 0 A U ^ 
U 1 ^ \ Z X 

H'N' Z' 
X' C' 

E u e 

U Z 


A U <|) 
\ Z >1 










c4 (/) 

o 2 


n Y X 





n Y X 

A n 

O N 
K X 


n Y T 
A e 1 

O K 
K A 


R V 
L b 


p n 

u D 

P V 
L b 

p n 

u D 


R <t> 
L F 

C P M I 

C u n < 



Synemmendn Diezeugmendn HyperbolaeSn 

Z A ^ r BA O' N' H' 

C 3 X N / \ \ K' »' >' 

Z A r B A J. O' N' H' 

C 3 X N / \ A K' >' >' 

Z A r B ^ X O' K' H' 

C \ X N /X A K' A' >' 

©r U Z EUOaM'I' 

V N Z C U Z A 1' <' 

E 2 




IS (A 

S g 



4 > 

4 > 


I • 




ri 7 n V T 

3 H r t =1 



c n K 

C D A 

H Y 1 X T 

a r \ ^ 

C O K 
C K A 





- 7 F V <() 
E I- J. H F 




Y T M 

u- 1 n 

' bbf - 


7 F Y <J) 
I- i. H F 

^ - * 

Y T M 

u- 3 n 

7 F n <j) 

t- ± A F 

Y n M 

u- D n 



Synemmendn Diezeuginen6n Hyperbolaedn 

AH r i ©ru*j.M' 

-<>N<VNZ X\n' 






S c 
- g 

o I 



- X 


4 > 

c 4 




c 4 



c 4 






4 > 




4 > 

c 4 





C 4 













W ri 7 y X 
h 3 (- H n 





<D T O 
F H K 



W ri 7 Y X 
h 3 h H A 

0 T O 
F 3 K 






N ri 7 n X 

h 3 h r n 

<D C O 
F C K 

rJ . Yi^~ 




M - mrijfiyxn 

H Euj3A't''\3 


F" I 



M - mrinYXn 

fl Eaj3^C''\3 

M - rny^^'l'Tn 

R EiuH/' ^ 3D 



Diezeuginen6n Hyperbolae6n 



















0 ) 









4 > 




4 > 





C 4 









-& - X 4 





? 3 : 



H hxrir LtC 



M 0 

1 1 

1 ^ ^ 


1 ^ 1 

owvi^n RVC 

H hxrir LtC 


--■ 1 --^ ■ . ^ ■ . - 

^ ^o 

^ 1 


IP _ ~~n~ _ 

















-2 ® 
^ g 

w 5 

o 2 


9 hN n 
H U R 


9 M 

F Y 4 > 
± H F 


9 m- 

F n 4) 

± A F 



3 H H 

7 Y X 


n 9 M 

3 H R 

7 Y X 
h- H n 


n 9 w 

3 H h 

7 1 X 

h- r n 






<j)C O TCO"?! ZA 










Hypate v 


Lichanus j 















1 /T-TiN • 

1 _ 


/ _1 

_ CJ 


- X:0 

w \ ^ ^ 

^3b|j — iT>rin 

q.£(U3 E lu3A 



r A - 

-• I2jg' ' 


—. .jLh. -^—(J 



^3 bu — n>Hn 

fl-£a)3 E iij3A 





3 b M - 

£ CO P E 

m Y n 

111 H 

6 o 


yrn <|>Yn maht 

C Fu-O n<i>N 



32. At this stage then the musical science of Greece 
found the material of all musical composition in a cer¬ 
tain number of two-octave scales, uniform in construc¬ 
tion, in the order of intervals, in the relation of the other 
notes to the tonic, but constituting in pitch a regular series 
spaced by equal intervals, admitting also theoretically the 
three genera of Enharmonic, Chromatic, and Diatonic, 
though the two former would seem to have fallen into 
practical disuse. And these scales may be resolved into 
the following elementary relations:— 

(a) The relation between a note and its octave above 
or below; 

( 3 ) the relation of a note to its Fourth above; 

(f) the relation of a note to its Fifth below; 

(//) the relation of two passing notes to the extremities 
of a tetrachord determined in so far that of the resulting 
intervals the lowest must be less than or equal to the 
middle, and less than the highest. 

The scheme of these scales, as has been already said, 
must not be identified with either our major or our minor 
mode. In the Greek scale of the Diatonic genus the notes 
follow one another, it is true, at the same distance as in 
our descending minor scale, but the Svvafus or function of 
the notes is different, and the essence of a note is its 
function. The essential feature of our minor scale is the 
concord of the Minor Third which makes part of its 
common chord; and this was to the Greek ear a discord, 
that is, a sound-relation not to be immediately recognized 
or permanently acquiesced in, but demanding resolution 
and change. 

33. We have seen that in this conception of the keys 
the distinction of modes is virtually ignored. But it was 
destined to be revived by the revolution in musical science 
which was effected by Ptolemy, the celebrated mathema¬ 
tician of Alexandria. This theorist observing that, by the 
extension of the modes illustrated in Table 21, their distinc- 



live feature of supplying certain segments of the common 
scale for the use of composers and performers had been 
sacrificed, reduced them again to their original compass; 
and, to emphasize the fact that their very nature forbade 
their extension, he introduced (or made popular) a new 
nomenclature by which the several notes of any mode were 
designated in relation to that mode only, and not in relation 
to the common scale of which they were all segments. 
Thus the terms Hypate, Parhypate, Lichanus, Mese, Para- 
mese. Trite, Paranete, and Nete were employed to signify 
the First, Second, Third, Fourth, Fifth, Sixth, Seventh, and 
Eighth notes of all the modes alike. These names were dis¬ 
tinguished from those of the old system by the addition to 
the former of the term Kara Becriv ‘ in respect of position,’ and 
to the latter of the term Kara Bvvafuv ‘ in respect of function.’ 

TABLE 23 . 


Kara hwa^uv ^ 



Kara Oiffiv ^ 



Kara hvvafuv 






Kard. Oiffiv tS 


Phrygian ® 

M a 
c ** 

mroL Suvafuv Ja a, 

2 W 



/card BkciV « 


Dorian ® 




























S2 c 
c (o 

/car^ hivafiiv 



Paranete ^ Nete "^“^^Waean ^ §> ^ Paranete 


Diezeugmen6n Hyperbolaedn 

But even in this innovation we are not justified in tracing 
any new sense of the possibility of different modalities. 
For Ptolemy himself asserts that the object of passing from 
one mode to another is merely to bring the melody within 
a new compass of notes. 

At this point we may close our investigation, as the 
further development of musical science belongs to the 
history of Modern Europe. 

34. For the sake of conciseness I have adopted in the 
preceding paragraphs the somewhat misleading method of 
presenting, in the form of an historical statement, what is 
in reality a mere hypothesis. For the same reason I have 
omitted details, and restricted myself to the most general 
features of the development. The latter of these deficiencies 
will to some extent be made good in the notes on the text 
of Aristoxenus; the former demands our immediate atten¬ 
tion. Strict demonstration of the truth of our hypothesis is 
in the nature of the case impossible; but we must at least 
examine the rival hypotheses and satisfy ourselves that the 
facts which tell fatally against them leave it unassailed. 
At the same time we must not be disappointed if many facts 
remain unexplained. In the development of any branch of 
human activity there is much that is accidental; accidental, 
in the sense that the explanation of it is not to be found 
inside the sphere of that activity. We shall be satisfied 





then if we find that our hypothesis accounts for many of the 
recorded facts, and is not irrefragably refuted by any of 
them; while the other intrinsically possible hypotheses— 
there are but two—are put out of court by the weight of 
unanswerable argument and evidence. 

35. Of one of these hypotheses the essential thesis is that 
the seven modes of Table 16 differ from one another as do 
our major and minor scales, that is in modality, or in the 
relations which the other notes of the scale bear to the 
tonic. The tonic of each scale it finds in the fourth note 
from its lower extremity, the /t€(n/ Kara Oecriv of Ptolemy. 

According to this view the seven modes and their tonics 
may be represented in the following Table. In (a) the 
scales are given in the Greek form, with the tonic in the 
Fourth place from the bottom; in (d) they are given in 
modern form, and start from the tonic. 

TABLE 24 . 



(ci) Mese 


(^) Tonic 





36. We cannot deny that at first sight this theory has 
much to recommend it. It affords an adequate explanation 
of the striking names bestowed upon the seven modes; for 
if these differed in modality, they certainly deserved distinc¬ 
tive titles. It enables us too, on the analogy of our major 
and minor scales, to conceive how the Greeks might have 
found in each mode a distinctive Ethos or emotional char¬ 
acter. Doubtless the objection at once presents itself that 
the ancient nomenclature of the notes recognizes no such 
variety of modality, that the note before the disjunctive tone 
is the Mese in every scale, no matter what its place therein 
may be. But this objection the theory finds little difficulty 
in answering. For it is quite permissible to suppose that 
one mode, because it was most common or most ancient, 
or for some other reason, was regarded by the theorists as 
typical, and that the nomenclature of the notes, originally 
applicable to that scale only, came to be applied at a later 
date to scales of different modality. Besides we have 
seen that, in the time of Ptolemy, if not earlier, there was 
a second system of nomenclature by which notes derived 
their names from their positions in their^respective scales, 

F 2 67 


and according to this system the fourth note of every scale 
was its Mese. 

37. Nevertheless this plausible hypothesis is absolutely 
untenable, as the following considerations will show. 

In the first place we must note that the modes are not 
the invention of theorists, but scales in practical use. Now, 
it is hardly conceivable, and in the absence of evidence or 
parallel wholly incredible, that an early and undeveloped 
artistic impulse should have produced such a variety of 
modalities, so many distinct languages, as one might say, 
of musical expression, not distributed through different 
regions and races, but all intelligible and enjoyable alike to 
a Hellene of Hellas proper. 

In the second place, the distinction which is here sup¬ 
posed between the modes is essential not accidental, and as 
such, it is wholly impossible that it should have been over¬ 
looked by the Greek theorists, who have proved themselves 
•in other respects the most subtle of analysts. Yet in all the 
extant authorities there is not one hint of such a distinction. 
Nay, we might go further and say that we cannot admit this 
hypothesis without convicting these theorists of a radically 
false analysis. If the tonic of the scale 

is C, the scale must divide itself into the tetrachords 


in which c, d, and g are the fixed, and a, e, and f 

the passing notes. But the theorists recognize no tetra- 
chord of either of these forms; but insist that in all tetra¬ 
chords of which fhe extreme points are the fixed notes, and 
68 . 


the inner the passing notes, the lowest interval must be less 
than the highest, and equal to or less than the middle. To 
take one from the countless instances we read in the 

Isagoge (Meibom, 3. 4): 

Vivyj S4 ioTL rpia, Siarovov, ap/tovia, Kal to 

fjiev Stdrovov iirl fjih/ to ^apv Kara rovov Kal tovov koX 'q/JUTOVtov, 
hrl Sc TO o^v ivavTtws Kara yfitrovLOV Kal rovov Kal rovov. to 
Sc ^TTi fJih/ TO ^apv Kara rpvqpLiroviov Kal '^puTovtov Kal 

ripiVTOVLOV, iirl Sc to o^v ivavriios Kara Tipuroviov Kal riparovLOV 
Kal rptripiLTovLOV. 17 Sc appiovia iirl piv to jSapu Kara Strovov Kal 
oi€criv Kai oucriVj ctti oc to ofu evavrtcos Kara dieortv Kat oteatv 


Here we find a certain order of the intervals of the tetra- 

chord affirmed without qualification. This affirmation 
implies that all diatonic scales can be reduced to com¬ 
positions of tetrachords of the form 

if C be its tonic could not be so reduced except by an 
analysis extending to the superficial qualities only, and 
leaving the essential nature untouched. 

Take again the following passage from the Isagoge 
(Meibom, 19. l) dTro Se r^s fieo'rjs Kal twv Xoiir&v ^^dyywv al 
Bwd/JieiS yvmpi^ovTai, to yap irws €^€1 eKoaros avrSiv tt/jos 
pAarp' (f>av€pS)s yiyverai. ‘ It is from the Mese that we start 
to discern the functions of the other notes; for plainly it is 
in relation to the Mese that each of them is thus or thus 

Or this still more striking passage from Aristotle 
{Problems, xix. 20): 



Ata Tt, iav yu.ei' T6S t^v fiicrqv Kiv^crp yfimv, apfioa-a^ rots 
aAAas )(opods, Kal ^p^Tou. t<S opydvio, ov fwvov orav Kara tov t^s 
lJi.€a~r]s yevrjrai, <p66yyov, \virei Kal <f>aCv€Tat dvap/warov, dAAa 
KoX Kara. Trjv d\X.r}v p.e\(aouLV’ idv oe ttjv Xi^avov ^ rtva aXKov 
<f>66yyov, Tore <f>aiV€Tai, oia<f>€peiv povov, orav Kojceivy tis xprjrai; 
—-*11 evXoyws TOVTO <rvp^aiv€i; irdvra yap to, y^pyjord peXrj 
■jToXXaKts rfj pecrp ^(p^ai, Kal TraKres oi dyaOol iroirjral TrvKvd 
irpds T^v picrrjv diravrUia'i, Kav aTriXSoKn, Taj(u ciravcpYovrat, 
irpbs o€ SXXtjv ovtws ovBepiav. KaOdirep ck twv Aoywv evCmv 
i^aipedh'TdiV <rvvB€(rpu)v ovk icmv o Aoyos *EAX'»/V6Kos, otov to 
T€ Kal TO Kai. mo6 ok ov$kv Xmovari, Bid to to6S pkv dvayKcaov 
eivai ^(f^<r$ai •jroAAaKts, el ecrrai Aoyos, Tots Be pyj. ovrw Kal twv 
<f>66yy<t)v y/ pecrrj uxnrep crvvBeiTpos eari, Kal pdXurra twv koXwv, 
Bid TO TrAciOTaKis iwirdp)(eiv tov <j}66yyov avrrj^. 

[Translated by Mr. Monro, Modes of Ancient Greek Music, 
p. 43: ‘ Why is it that if the Mese is altered, after the 

other chords have been tuned, the instrument is felt to be 
out of tune not only when the Mese is sounded, but through 
the whole of the music—whereas if the Lichanus or any 
other note is out of tune, it seems to be perceived only 
when that note is struck? Is it to be explained on the 
ground that all good melodies often use the Mese, and all 
good composers resort to it frequently, and if they leave it 
soon return again, but do not make the same use of any 
other note? Just as language cannot be Greek if certain 
conjunctions are omitted, such as re and Kai, while others 
may be dispensed with, because the one class is necessary 
for language, but not the other; so with musical sounds the 
Mese is a kind of “conjunction,” especially of beautiful 
sounds, since it is most often heard among these.’] 

It is hard to imagine how the nature of a tonic could be 
more clearly and truly indicated than it has been by the 
author of this passage in his description of the Mese. And 
as he expressly states that the Mese is the centre of unity 



in all good music, he must have recognized only one 
modality. An attempt has, indeed, been made to evade 
this conclusion by supposing Aristotle to refer not to the 
ixecrr) Kara Bvvafjiiv, but to the fiecrr] koto. 6€(T(v. But this 
supposition is quite untenable, not only because the nomen¬ 
clature Kara 6 i(rtv in all probability was the invention of 
Ptolemy, but also for this much more convincing reason that 
the terms Kara Bvva/uv and Kara dea-iv seem framed with the 
direct intention of precluding such a supposition. The 
txearrj Kara dia-iv is merely the note which is located in the 
centre of a group; the it.€<rq Kara Swa/uv is the note which 
discharges the function of a centre of unity to a system. 
The first is a mathematical, the second a dynamical centre. 
When, therefore, the whole train of Aristotle’s reasoning is 
based on his conception of the Mese as the connecting 
bond of musical sounds, can there be any manner of doubt 
to which Mese he refers ? 

38. Again, we have seen that one attractive feature of this 
hypothesis is that it offers a plausible explanation of the fact 
that the Greeks attributed a distinct Ethos or emotional 
character to each of the modes. It now remains to show 
that this plausible explanation is refuted by the express state¬ 
ment of the authorities as to the conditions of this Ethos. 

Consider the following passages:— 

(a) Plato, Republic, iii. 398 e: 

Tfvcs ovv Opyp/dBeis apfiovuu; . . . Mt^oXvotarf, e<f>rj, Kal 
^vvtovoXvBlotI Kal Toiavrax t6Vcs. —TtVcs ovy p,a\aKai re Kal 
crvuTTOTiKal Twv a.ppx>viS>v; ’laort, ^ o os, Kal AvBujti, alrives 
voAapal KoXovyrai,. 

‘ What then are the scales of mourning ? ’ ‘ Mixolydian,’ 

said he, ‘and High Lydian, and some others of the 

same character.’ ‘Which of the scales then are soft and 

convivial?’ ‘The Ionian,’ he replied, ‘and Lydian, such 
as are called slack ’ (i.e. low-pitched). 



{l>) Aristotle, Politics, vi (iv). 3. 1290 a 20: 

0/Aowos 8’ Trepi ras dp/tovias, ws <j>aar[ t 6V€S' xal yap 

€K€i Tidevrai et^rj Svo, Tr]v Awpcort Kal Tr)v ^pvyiarC, to. 8e aXka 
(TwrdypMTa tol p-ev ^dpux tol Se ^pvyia KoXovcnv. p-aXiara piev 
ovv €l<a$a<riv ovtws VTroXap.^d.veiv Trepi twv iroXtreiw' aXyiOearrepov 
8k Kal piXTiov <t)s StctXo/tcv 8volv ^ pads ovaijs Trjs KaXS>s 

(TwearrjKvCas tol? dXXas civai irapeK^dareis, ras pi-kv t^s tv k€- 
Kpapiivrfs dppMvias, ras 8k rrjs dpicrrqs TroXiTeCas, oXiyap^^tKas pikv 
rds (rvvTovorrepas Kal StcrTroTiKwWpas, rds 8’ dvti/ttvas Kal 
ju.aA.aKds 8r}piOTiKds. 

‘ Some would have it that it is the same in the case of 
scales; there too they posit two species, Dorian and 
Phrygian, and all other systems they class as either one or 
the other of these. Such is the common view of forms of 
government. But our analysis was truer and more satis¬ 
factory, according to which of perfect systems there are but 
one, or two, while the rest are deviations, in the one case 
from the scale of proper composition, in the other from the 
best possible government; those that incline to high pitch 
and masterfulness, being of the nature of oligarchy, those 
that are low in pitch and slack being of the nature of 

{c) Aristotle, Politics, v (viii). 5. 1340 a 38 : 

Ev0vs yap r/ tS>v appovidv 8i€crrrjKe (f>v<ris uxrre aKovovras 
aXXms 8iaTi6e<r6ai koI prj t6v avrov ex®*’’' 'rpoTTOv wpds iKaarrjv 
avTmv, aXXjd wpos pkv ivias ■o8vpTtKa)T€po)s Kai (rvvearrjKOTws 
pidXXov, oiov TTpbs TTjv Mt^oXv8toTi KaXovpivrjv, irpbs 8k rds 
paXaK<i)T€pms rrjv 8idvoiav, otov Trpbs Tas dveipJvas. 

‘To begin with there is such a distinction in the nature 
of scales that each of them produces a different disposition 
in the listener. By some of them, as for example the 
Mixolydian, we are disposed to grief and depression; by 
others, as for example the low-pitched ones, we are dis¬ 
posed to tenderness of sentiment.’ 



{d) Aristotle, Politics^ v (viii). 7. 1342 b 20 : 

Otov TO?s ojruprfKoa'L hia ')(p6vov ov paZiov ^Seiv ras owrovovs 
apfJLOvCa^, aXXa ras aveifx.€va^ fj <pv(ri^ VTro^dXXei rots TT/XcKovrots. 

‘ Thus for those whose powers have failed through years 
it is not easy to sing the high scales, and their time of life 
naturally suggests the use of the low.’ 

From these passages it is clear in the first place that the 
Ethos of the modes was dependent on their pitch, and in 
the second place that the pitch on which the Ethos depended 
made them severally suitable for voices of a certain class or 
condition. But, if the distinction between the modes is 
one of modality in our sense of the word there is no reason 
in the nature of things why they should differ in pitch at all. 
And though we might assume for them a conventional dis¬ 
tinction in pitch by regarding them theoretically as fragments 
of one typical scale shifted from one point of pitch to 
another, the assumption would not help us to meet the facts. 
A conventional distinction of pitch cannot be the basis of 
an absolute distinction of Ethos, nor can' it account for 
the practical suitability of certain scales to certain voices. 

39. The weight of these arguments is so irresistible that 
we are not surprised to find Mr. Monro substituting a new 
hypothesis in his Modes of Ancient Greek Music. Un¬ 
fortunately this substitute, though it embodies one most 
important truth, is open itself to objections no less grave. 
The fundamental principle from which Mr. Monro’s theory 
starts is that the Greeks knew but one modality, that is one 
set of relations between the notes of a scale and its tonic; 
and the establishment of this principle by argument and 
evidence is the great contribution of Mr. Monro to the study 
of Greek Music. Proceeding from this principle, he main¬ 
tains that the terms Dorian, Lydian, Phrygian originally 
designated merely so mkny k^Sy that is so many scales 
identical in their intervals and in the order of them, but 



differing in pitch. The connexion of these names with 
certain modes or scales of different figures arose in his 
opinion at a later period from the fact that practical limita¬ 
tions restricted composers and performers to a certain 
compass, and the name of the key was transferred to the 
particular order of notes which it afforded within that com¬ 
pass. Thus the term Mixolydian and Dorian originally 
denoted the two keys 














_ m-M _in_ 



-0 _ 


Now suppose that a composer or 
performer was restricted to the par¬ 
ticular compass 

Within that compass the Mixolydian key would give the 

_Q_ rk _ 


which is of the form 






■ fiiimmmmmmmm 





mmtr .mm 


and in this way the terms might come to be applied to 
certain orders of intervals. 

40. The objections to this theory are many and fatal. At 
the very outset, we are repelled by the supposition that such 
a striking nomenclature should have been adopted to denote 
such a superficial difference. Again, how are we to explain 
the,distinct ethical character of the scales? If the pitch of 
the Dorian, Phrygian, and other keys be only determined 
by their relation to one another, their emotional character 
must also be only relatively determined; if, for example, 
high pitch is the natural expression of pathos, we can say of 
the higher of two keys that it is more pathetic than the 
lower, not that it is absolutely pathetic; yet the Greeks 
always attribute an absolute character to each of the scales. 
It would follow that the pitch of the keys must have been 
absolutely determined. But of such absolute determination 
there is not a word in our authorities. Even if we assume 
it, in spite of their silence, surely it cannot have been exact. 
Absolute and exact determination would presuppose the 
universal recognition of a conventional standard embodied 
in some authorized instrument, or expressed in a mathe¬ 
matical formula; the first alternative is precluded by its 
absurdity, and there is no evidence for the second. But 
if the determination, though absolute, was not exact, while 
we might admit an absolute difference of Ethos between 
a scale of extreme height and one of extreme depth, there 
could have been no such absolute difference between scales 
separated only by a tone or semitone ; for let there be but 
a slight variation between the tuning of one day and another, 
and the Phrygian of to-day will be the Lydian of to- 



morrow. And even if we make Mr. Monro a present of all 
these objections, and grant the existence in ancient Greece 
of an absolute and exact determination of pitch, will any 
one venture to affirm that the difference of a tone or 
semitone in the pitch of two keys could result in such an 
antagonism in their moral effects, that Plato should have 
retained one of them as a valuable aid to ethical training, 
while he banished the other relentlessly from his ideal 
republic ? 

Again, it is not uncommon^ to find the names of musicians 
recorded as inventors of certain scales. Would Mr. Monro 

have us believe that the only claim of these musicians to 
the regard of posterity is that they stretched the strings of 
their lyre a little more loosely or a little tighter than did 
their predecessors ? 

41. Returning now to the hypothesis which we have above 
proposed we shall consider a few passages which seem to 
offer striking confirmation of its truth. 

{a) Heraclides Ponticus apud Athenaeum, xiv. 624 c ; 

Hpa/cXecSiys 8’ o IIovt 6 kos iv Tpirta Trepi ^ovcnKrjs ou8’ 


<f>rjcn Beiv KaXeicrdat Trjv ^pvyiov, KaOdirep ovSe Trjv 

Avdiov, appovia^ yap elvai Tpcts* rpCa yap koI yeveaQai 'EAX'^vwv 

yevrj, Awptetv, AtoAcJs, *Io)vas • . . (625 d) KaTa<ppov7jTiov ovv twv 

Tas p.h' KOT €?8os 8ia^opas ov Svvap.€v<t)v dewpew, €‘jraKoXx)v6ovvTO)v 

^ For example see Plutarch, de Mustca, 1136 C-D 'ApiarS^evos Si 
Kprjai Scur</>di irpinTtjv evpaaBai Tr)V Mi(o\v5iffTi ... iv Si toTs 'laropiKoits 
Ttjs 'kp/wviKrjs Ili>0oic\eiSr]v tprjai rov av\t]7iiv e{/peT))v avT^s ytyovivai . . . 
aWcL prjv koI Tf)v 'Enaveipivr)v AvSiari, ijirep ivavrla ry Mi(o\vSiari, napa- 
irKtjffiav odaav ’IctSi vird Aapwvot evp^aOai <paci tov 'Adrp/aiov. 

17 ’EnaveipUvt] AvSiari, or low-pitched Lydian, is probably the same 
as the later Hypolydian. By the Ionian is probably meant the Hypo- 
phrygian, The Hypolydian in its schema, that is in the position of 
its tonic in relation to the other notes, is very similar to the Hypo- 
phrygian and most unlike the Mixolydian. 



8k T« t 5 )v <f>66yy(av o^yrryn Kal ^apvnjri koX riOefiivtav ’Yirep- 
p,i^oX.vBiov appuoviav Kat irdXcy virkp ravrtjs aWtfv . . . SeT 8k 
TTjv appuoviav cXSos i]6ovs y Trddovs. 

‘ Heraclides Ponticus in the third book of the de Musica 

asserts that the term dppuovia should not be applied to the 
Phrygian or Lydian scales ; that there are three Harmonies, 
as there are three tribes of Hellenes—Dorians, Aeolians, 
lonians . .. We must conceive a very low opinion of the 
theorists who fail to detect difference of species, while they 
keep pace with every variation of pitch and establish a 
Hypermixolydian Harmony and again another above that. 

. . . But every Harmony should possess an ethical or 
emotional character peculiar to itself.’ 

Mr. Monro, by a curious misapprehension, as I think, of 
this passage, has accused Heraclides of carrying Hellenic 
exclusiveness to the extreme of refusing the title of dppoviai 
to the oriental scales of Lydia and Phrygia. But the 
meaning of Heraclides’ statement is that the seven scales 
of Table i6, inasmuch as they are only so many segments 
of the one scale, are all instances of the one dppuovia or 
method of formation, and so cannot properly be termed so 
many dppuoviau It was a different matter, he says, with the 
three ancient Harmonies, the Dorian, Ionian, and Aeolian. 

These were really distinct adjustments; they were scales, 
the principles of whose construction were essentially dis¬ 
similar. Difference of pitch, he proceeds to say, does not 
constitute a new dppovia. 

{l>) Aristides Quintilianus (Meibom, 21. ii) : 

To pukv ovv AvSiov Bidcrrtjpua <rw€Ti 6 €(Tav ck Steo'ews, Kal 

Bitovov, Kal TOVOV, 

Kal Steo'ccos, Kal Biecrews, Kal Bitovov, Kal Sie- 

cr€(t)S' Kal TOVTO fjiev riXeiov OT^cmy/Aa, to Sc Aiaptov ck tovov, 
Kal Stecrews^ Kal StecrewSf Kal Sirovov, Kat tovov^ Kal Stcorcws, Kat 
St€(r€(us, Kat StTOVOv rjv Sc Kat tovto tovw to Sta Traawv wcpc^^ov. 

€ ^ovyiov 



Tovov, Kal Sl€(T€<ds, Kol 8ie(reo)S, Kal tovov Ijv Se Kal tovto reXeiov 
Ota iraatoy. 

* The Lydian scale they ’ [i.e. ancient musicians] ‘ composed 
of diesis, ditone, tone, diesis, diesis, ditone, diesis; this 
was a complete scale. The Dorian was composed of tone, 
diesis, diesis, ditone, tone, diesis, diesis, ditone; this scale 
again exceeded the octave by a tone. The Phrygian was 
composed of tone, diesis, diesis, ditone, tone, diesis, diesis, 
tone; this too was a complete octave.’ 

(c) The IsagogCy (Meibom, 20. i); 

AvBioi 8e 8vo, o^vTcpos fcal ^apvrepos, os Kai AloXios KaXeiTai’ 
^pvyioi 8vo, 6 p.h' Papx>%, os kol laoTtos* o S’ o^s. Atapios 
eii. ‘Yiro\v8ioi 8vo’ o^urcpos nai ^apvrepos os koX 'YwoacoXios 
KaXeiTai. i‘7ro<f>pvyioi 8vo, 5v o ^apvrepos Kai itroidcmoi 

‘Two Lydian keys, a higher, and a lower, also called 
Aeolian; two Phrygian, one low also called Ionian, and 
one high; one Dorian; two Hypolydian, a higher and a 
lower, also called Hypoaeolian; two Hypophrygian, of 
which the lower is also called Hypoionian.’ 

It appears from passage (a) that there was a period in 
the development of the Greek musical system when there 
existed three distinct Harmonies, i. e. three scales dis¬ 
tinguished by the different methods in which their units 
were put together; and that these three Harmonies were 
termed Dorian, Aeolian, and Ionian. Now the units of 
Greek music are the tetrachords; and we cannot conceive 
how tetrachords could have been put together except by 
the method of conjunction, the method of disjunction, the 
method of alternate conjunction and disjunction, or a com¬ 
bination of two or more of these methods. It is probable 
then that the three Harmonies were the products of these 
three methods. But the characteristic feature of the 
Dorian scale of Aristides Quintilianus (see passage {d)) is 


that it contains two disjunctive tones in succession; from 
which we may reasonably conclude that the Dorian Harmony 
was the method of disjunction. 

Again in passage (c) we find that when the number of 
the keys was raised from seven to thirteen, the terms Ionian 
and Aeolian were employed to denote respectively the 
duplicate Phrygian and Lydian keys. This implies a con¬ 
nexion for purposes of music between the terms Ionian 
and Phrygian, and between the terms Aeolian and Lydian. 

. But the Lydian scale of Aristides is plainly a scale of 
alternate conjunction and disjunction; and the characteristic 
feature of the Phrygian* is that it introduces the Fourth 
above as well as the Fourth below the tonic; in other 
words, that it retains the essence of conjunction. It seems 
a fair inference then that the Ionian and Aeolian Har¬ 
monies are identical respectively with the method of 
conjunction, and the method of alternate conjunction and 

(d) Plutarch, de Musica^ 1137 ^ 8 c koI to Trepl twv 

VTraTmv OTi ov 01 ayvouiv d'Trci^ovTO cv rots ^otplots tov rerpa- 

^ The mistake has commonly been made of explaining the upper 
tetrachord of the Phrygian scale 


> ^ _I__ 11 ^ _ 

rffn ^ 


1 ^Y- _ 




as a mixture of enharmonic and diatonic notes, d being the second 

passing note of the diatonic tetrachord 

But this interpretation ignores the distinction between fixed and 
variable notes, a distinction which Aristoxenus and other theorists 
are never weary of repeating. If d in the Phrygian scale were 
merely a passing note of the diatonic tetrachord, its position would 
not be exactly determined ; and as the lowest interval of the scale 
is exactly determined as a tone, the compass of the whole could not 
be definitely estimated as an octave. Besides, we should then have 
three passing notes in succession, and two Kixayoi; the impossibility 
of which will be obvious to any one who has grasped the Greek 
conception of a note as a dwafiis, not a point of pitch (see § 8). 



cJSoTcs' Sta Sc r^v tov ^6ovs <f>v\aK^v a<f>r}povv ivl tov AmpCov 
Tovov, Ti/twvTcs TO KaXov ovTov. ‘ With regard, too, to the 
tetrachord Hypaton, it is plain that it was not through 
ignorance that they’ (ot TraXaioi, the ancients) ‘abstained 
from this tetrachord in the Dorian Scale. The fact that 
they employed it in the other keys is proof that they were 
acquainted with it. But they dispensed with it in the 
Dorian because they respected the beauty of that key, and 
were determined to preserve its character.’ 

We saw above (§ 29) that to the early scale of the form 

was added at a later period a conjunct tetrachord at its 

lower extremity 

and that this 

addition was called the tetrachord Hypaton. In the pas¬ 
sage before us Plutarch informs us that for some time an 
exception was made in the case of the Dorian scale because 
it was felt that such an alteration would imperil its Ethos. 
Mr. Monro endeavours to reconcile this statement with his 
hypothesis of the keys by pleading that the character of 
moderation inherent in a key of middle pitch would be 
sacrificed by the addition to it of a series of lower notes. 
To which we may reply ‘ Would not the pathetic character of 
a high pitched scale suffer equally from such an extension? ’ 
But on our hypothesis Plutarch’s statement is quite in¬ 
telligible. Obviously the distinctive character of a disjunct 
scale would perish on the addition to it of a conjunct 

(e) See again the passage from the Politics of Aristotle, 

V (viii). 7. 1342 b, quoted in § 38. 



Aristotle here recommends the use of certain scales to 
voices that are impaired by age. What then must have 
been the special property of these scales, that justified this 
recommendation? Evidently not a particular modality, 
for one order of intervals does not involve a greater strain 
on the voice than another. Nor can it have been a mere 
difference of key or general pitch. How should the same 
keys suit the failing tenor, and the failing bass ? The pro¬ 
perty of these ‘ old men’s scales ’ must have been such that 
the melody composed in them, whatever the pitch limits of 
its compass might be, made but a slight demand on the 
physical powers. And this is the essential property which 
our hypothesis attributes to the Hypolydian mode for 
example. For whether that mode occur as the scale 


for a treble voice; or as the scale 

for a tenor voice; or as the scale 


for a bass voice; it necessarily results from the position of 
its tonic that any melody composed in it must gravitate 
towards its lower notes. 

42. Many persons are under the delusion that to solve 
the problem of ancient Greek music means to bring to light 
some hitherto overlooked factor, the recognition of which 



will have the effect of making the old Greek hymns as clear 
and convincing to our ears as the songs of Handel and 
Mozart Very curious is this delusion, though not astonishing 
to any one who has reflected on the extraordinary ignorance 
of mankind about the most spontaneous and universally 
beloved of the arts, and their no less extraordinary in¬ 
difference to its potent effects on the mental and moral 
character. Who would take up a book on Egyptian or 
Chinese painting in the expectation of learning from it sonle 
new knack of placing or viewing an Egyptian or Chinese 
picture, by which it will come to please the eye as much as 
a Titian or a Turner ? Who would demand from metrical 
science that it should supply us with some long-lost spell by 
the magic of which we shall discern in 

(pvvai rbv airavra vitca \ 6 yov rd 8*, €w€l <l>av^y 
^rjvai KHG* OTToOev 7 ]K€t iroXh d€VT€pov djs 

the movement of 

* We are such stuff 

As dreams are made on, and our little life 
Is rounded with a sleep/ 

Yet no less absurd is the supposition that any, even the 
most perfect, knowledge of facts could lead us to the love 
of these unfamiliar old-world melodies. 

To some cold appreciation of their form we may perhaps 
attain if we are willing—sacrilege and destruction as it may 
seem—to strip them of those external accidents which are 
peculiar to the music of their age, and invest them instead 
with the habits of modern fashion. Otherwise the novelty 
of the unfamiliar features will engross our ear to the 
exclusion of the essential form. To render an ancient 
melody note for note is to render it unfaithfully to ears 
unaccustomed to its dialect ; just as to translate an ancient 
poet word for word is to misrepresent him, inasmuch as the 

attention is thereby misdirected away from the sense to 


the strange idiom. Nay, further, as a literal translation 
may often give a directly false impression of the meaning, 
so strict adhesion to the notes of a foreign melody will 
often lead us astray as to its essential form. As Aristoxenus 
would say, in attempting to preserve the pitch, we are 
sacrificing the all important Swayous. If, for instance, we 
express the Greek enharmonic progression to the tonic 
through Hypate, Lichanus, Mese, by 

not only are our ears revolted by the unwonted progression, 
but we are even distorting the real form of the melody. 
For, to take one point only, the Lichanus being the highest 
of the passing notes to the tonic from the Fourth below is 
for the Greek ear the next note to the tonic; while we feel 
that in passing from F to A we are skipping several notes 
which the melody might have employed. 

Let us apply, then, this method of paraphrase to the 
familiar Hymn to the Muse, one of the compositions of 
Mesomedes, a Cretan musician who lived in the reign of 
the Emperor Hadrian, The words and ancient notation 
(as far as it is extant) of the hymn are as follows :— 

c z 



(t> (t> 

C C 

•'A - €1 . 

• $€ 


-(7a fJioi 

<l>( - \rj 


<D M M 




Ka - rdp-x^^t 

Z Z 


E Z 

H H 1 

av - prj 


( 7 WP an 

aX- ai -ojy 

M Z 



0 C 


M <tC 

e - n 


a s 


- vas 


• - l - TCJ 

C P 


P C 

0 C 

KaA*Ac - 0 - TTCi - o <ro - <pd, 

G 2 


(D H 



C C C "1 




- wv 

irpo • fca -Oa - yi - ri 


- vwv 


0 C 

P M 1 M 


(70 - <p\ 

fJLVa - TO - 5(5 - TO, 

M 1 



r M p 



Aa - rovs 70 - 

Atj - Ai • € 



M 1 

Z M 

1 <J) c c 

€V-fC€ - 

•V € T s 

irdp*€(T~Ti fJLOl 

We shall {a) substitute for the Greek modality our major 
scale; (b) substitute Diatonic notes for those of other 
genera ; {c) add simple harmonies ’; (d) make slight altera¬ 
tions in the melody so as to preserve as easy a progression 
in our major scale, as is the original progression in the 
Greek scale. 

Hymn to the Muse. 



^ Professor Prout has supplied the harmonies ; but he is not other¬ 
wise responsible for this well-intended mutilation. 




B.—On Aristoxenus and his extant works. 

I. Our knowledge of the musical theory of Ancient 
Greece we owe almost entirely to Aristoxenus, or the Musi¬ 
cian (such is his regular title in ancient writers). This philo¬ 
sopher was born' in Tarentum, and received his earliest 
instruction from his father Spintharus (also called Mnesias), 
a well-known musician of that town, who had travelled 
much, and come into contact with many of the great men 
of the day, and, among others, with Socrates, Epaminondas, 
and Archytas. Some part of the youth’s life was spent in 
Mantinea, the inhabitants of which city were remarkably 
conservative in their musical tastes; and it was probably 
from this sojourn, as well as from the teaching of Lamprus 
of Erythrae, that he derived his intense love for the severity 
and dignity of ancient art. On his return to Italy he 
became the pupil and friend of the Pythagorean, Xeno- 
philus of Chalcis. Something of the austerity of this school 
seems to have clung to him to the last; he bore, for 
example, the reputation of having a violent antipathy to 
laughter! We next find him in Corinth, where he was 
intimate with the exiled Dionysius. From the lips of the 
tyrant he took down the story of Damon and Phintias, 
which he incorporated in his treatise on the Pythagoreans. 
Lastly we hear of him as Peripatetic and pupil of Aristotle. 
His position in this school must have been one of import¬ 
ance ; for he entertained hopes of succeeding the master, 
and his disappointment and disgust at the selection of 
Theophrastus betrayed him into disrespectful language 
towards the mighty dead. Indeed, if report speaks truly, 
want of reverence must have been his besetting sin; he 

* For everything that is known about the life of Aristoxenus, and 
for the references to the ancient authorities, see the excellent article 
in Westphal’s Aristoxenus, vol. ii, pp. i-xii. 



would seem to have consistently undervalued Plato, and to 
have maliciously propagated scandalous stories, which he 
had gleaned from his father, about the domestic life of 
Socrates. Besides his works on musical theory he wrote 
philosophy and biography. 

2. The signal merits of this philosopher do not flash upon 
us at the first reading of him. The faults of his style are so 
glaring—his endless repetitions, his pompous reiterations of 
‘ Alone I did it,’ his petty parade of logical thoroughness, 
his triumphant vindication of the obvious by chains of 
syllogisms—that we are apt to overlook the services which 
such an irritating writer rendered to the cause of musical 
science. And yet these services were of great importance ; 
for they consisted in no mere improvement of exposition, 
in no mere discovery of isolated facts, or deeper analysis 
of particular phenomena, but, firstly, in the accurate deter¬ 
mination of the scope of Musical Science, lest on the one 
hand it should degenerate into empiricism, or on the other 
hand lose itself in Mathematical Physics; and secondly, in 
the application to all the questions and problems of Music 
of a deeper and truer conception of the ultimate nature of 
Music itself. And by these two discoveries it is not too 
much to say that he accomplished a revolution in the 
philosophy of the art. 

Until Aristoxenus appeared upon the scene the limits of 
Musical Science had been wholly misconceived. There 
existed, indeed, a flourishing school of Musical Art; there 
was conscious preference of this style of composition to 
that ; of this method of performance to that; of this con¬ 
struction of instruments to that ; and the habits formed by 
these preferences were transmitted by instruction. To 
facilitate this instruction, and as an aid to memory, recourse 
was had to diagrams and superficial generalizations; but 
with principles for their own sake the artist, empiricist as he 



was, did not concern himself, and it is with principles for 
their own sake that science begins. 

Over against these empiricists there stood a school of 
mathematicians and physicists, professing to be students 
of music, and claiming Pythagoras as their master, who were 
busied in reducing sounds to air vibrations, and ascertaining 
the numerical relations which replace for the mathematical 
intellect the sense-distinctions of high and low pitch. Here 
we have a genuine school of science, the soundness of 
whose hypotheses and the accuracy of whose computations 
have been established by the light of modern discovery. 
Nevertheless, musical science was still to seek. For if the 
artists were musicians without science, the physicists and 
mathematicians were men of science without music. Under 
the microscope of their analysis all musical preferences are 
levelled, all musical worth is sacrificed ; noble and beautiful 
sounds and melodies dissolve, equally with the ugly and base, 
into arithmetical relations and relations of relations, any one 
of which is precisely as valuable and as valueless as any other. 
True musical science, on the contrary, accepts as elements 
requiring no further explanation such conceptions as voice, 
interval, high, low, concord, discord ; and seeks to reduce 
the more complex phenomena of music to these simple 
forms, and to ascertain the general laws of their connexion. 
Yet, while it will not be enticed to transgress the limits of 
the sensible, within those limits it will aim at thoroughness 
of analysis, and completeness of deduction. Such is the 
science which Aristoxenus claimed to have founded. 

And with this clearer perception of the scope of musical 
science there came also a deeper conception of music itself. 
So busy were the Pythagoreans in establishing the mere 
physical and mathematical antecedents of sounds in general, 
that they never saw that the essence of musical sounds lies 

in their dynamical relation to one another. Thus they 


missed the true formal notion of music, which is ever 
present to Aristoxenus, that of a system or organic whole 
of sounds, each member of which is essentially what it does, 
and in which a sound cannot become a member because 
merely there is room for it, but only if there is a function 
which it can discharge. 

The conception, then, of a science of music which will 
accept its materials from the ear, and carry its analysis no 
further than the ear can follow; and the conception of 
a system of sound-functions, such and so many as the 
musical understanding may determine them to be, are the two 
great contributions of Aristoxenus to the philosophy of Music. 

3. Suidas credits Aristoxenus with the authorship of 453 
volumes. Of these nothing considerable has survived save 
an incomplete treatise on Rhythm, and the so-called ‘Three 
Books of the Harmonic Elements.’ That the last title is an 
erroneous one has been established by Marquard and 
Westphal, who appeal to the following facts among others. 

{d) Porphyry cites the first of these books as irpwTo^ Trepl 
ap)(iuv, and the second as irpcoTos tSv dppxwiKmv oroiYewov. 

(d) Though the usual titles of these three books are 
supported by most of the MSS., there are some important 
exceptions. The Codex Venetus (M) has for initial title 
of the first book Apurro^h'ov Trpb twv appaviKtav <ttoi^€io)v 
( though a later hand has crossed out wpo twv and added 
TrpwTov), and similarly the Codex Barberinus reads irpo twv 
dp/AoviKwv -n-pSyrov. The concluding inscription of this book 
in M is 'ApuTTo^fvov to w-pfirov crroixelov, but the third hand 
has written Trpo twv over trpwTov, and to over the latter o of 
oTotxeiov. In the same MS. the title of the second book is 
*ApurTo$€vov dppiovLKiov oToixeucv (the (0 in the latter words' 
is a correction of the second hand for o) but an a has 
been written through the ^ by a later hand; the concluding 

inscription of the same book is ' Apiaro^ivov oroi^twov dpp,ovi- 



k 5 )v a, but the a is crossed out, and written beside it; the 
heading of the third book is 'Apurro^evov crTOL)(€Ut)v appovLKuiv 

with the crossed out and y written beside it. 

(c) The text of the ‘ Three Books ’ contains matter of 
three distinct classes ; firstly, introductory matter or exposi¬ 
tion of the scope and divisions of the subject; secondly, 
general principles or expositions of primary laws and facts; 
thirdly, propositions of details, following one another in 
logical order like the crToix«a or Elements of Euclid. 

(d) We find in several cases more than one treatment of 
the same subject. 

(e) We find certain inconsistencies. Thus p-ekoTroua, or 
musical composition, is sometimes included in, and some¬ 
times omitted from, the list of objects with which Harmonic 
science is concerned. 

Westphal, not content with negative criticism, has en¬ 
deavoured to reconstitute from the extant fragments the 
scheme of three, works of Aristoxenus on the Theory of 
Music; each containing a irpooipxov or introduction, a state¬ 
ment of a.pxo-1 or principles, and a system of aroixeia or 
elementary propositions. His idea may well be correct; 
but the result is so unsatisfactory from the utterly frag¬ 
mentary nature of the data, that we need not enter into the 
details of his attempt. 

4. The most important MSS. of the ‘ Harmonic Elements ’ 
are the following: 

The Codex Venetus (in the Library of St. Mark), written 
by one Zosimus in Constantinople in the twelfth century. 
It has been corrected by many hands; but two of especial im¬ 
portance have been identified, one older than the fourteenth 
•century (denoted in the Critical Apparatus by Mb) and one 
of that century or later (Me). Ma denotes the first hand; 
Mx a hand not identified; (a later manuscript in the same 
library is denoted by m): 



The Codex Vaticanus of the thirteenth and fourteenth 
centuries, which appears to have been directly copied from 
M. In the Critical Apparatus the first hand of this MS. 
is denoted by Va, a corrector by Vb: 

The Codex Seldenianus (in the Bodleian Library), dating 
from the beginning of the sixteenth century. It is denoted 
by S in the Critical Apparatus. Mr. H. S. Jones has 
demonstrated {Classical Review, VII. lo), that this 
MS. depends closely on V throughout, though its exact 
relationship is hard to determine, since in some places it 
adheres to the original reading (Va), and in others adopts 
the corrections and additions of Vb. I have collated this 
MS. afresh: 

The Codex Riccardianus (in Florence) of the sixteenth 
century (collated by van Herwerden), which shows relation¬ 
ship with Me: 

The Codex Barberinus (in the Bibliotheca Barberina in 
Rome) of the first half of the sixteenth century. From 
page 95 to 121 of the text this MS. shows agreement with 
Me and R; but from page 121 on, it appears to have been 
copied from V after the corrections of Vb. This MS. has 
numerous corrections in the margin, which, however, are in 
the same hand as the original: 

A Codex of great value which belonged to the Library of 
the Protestant Seminary at Strassburg, and perished when 
that building was burned down by the German troops on 
the night of August 24,1870. It was collated by M. Ruelle, 
who published the results with his translation of Aristo- 
xenus. It seems to have been independent of all the other 
MSS. that we possess, none of which can be regarded either 
as its ancestor or its descendant. M. Ruelle attributes it 
to the fifteenth century. It is denoted by H in the Critical 

The ‘ Harmonic Elements ’ were first published at Venice 



in 1542, in a Latin translation by Antonins Gogavinus, 
a worthless work crowded with errors. The first edition 
of the Greek was printed in Leyden in 1616 by Elzevir, 
with the corrections and commentary of Johannes Meursius, 
who displays gross ignorance of the general theory of Greek 
music, and of the doctrine of Aristoxenus in particular. 
Meibom’s well-known edition with the Greek text, Latin 
translation, and commentary, was published in 1652 at 
Amsterdam by Elzevir. The text of this work is poor and 
the translation often obscure, but the commentary is valuable, 
and shows a thorough acquaintance with the system of 
Aristoxenus. Paul Marquard’s edition with a German trans¬ 
lation (so literal and servile as to be wholly useless) was 
issued at Berlin in 1868. The chief value of this work lies 
in the new light thrown on the text by the author s collation 
of the Codex Venetus. Westphal’s exhaustive but diffuse 
and garrulous book on Aristoxenus was published at Leipzig 
in two volumes, the first in 1883, and the second in 1893, 
after the author’s death. It is most valuable as a storehouse 
of facts. M. Ruelle’s French translation of Aristoxenus, 
to which I have referred above, was published in Paris in 

The following authors and works are referred to in the 
present volume: 

The Ela-aymyrj apfioviK-q (referred to in this volume as 
Isagoge) formerly attributed erroneously to Euclid (and so 
inscribed in Meibom), but probably the work of one Cleon- 
ides, of whom nothing else is known. It exhibits a strong 
resemblance to the doctrine and arrangement of the ‘ Har¬ 
monic Elements ’ of Aristoxenus : 

Nicomachus of Gerasa, who flourished in the second 
century, a. D. ; a Pythagorean mathematician, and musician; 
author of a manual of Harmonic : 

Bacchius Senex, a musician of the time of the Emperor 


Constantine. The so-called ‘ Introduction of Bacchius ’ is 
a mass of excerpts of unequal value, some showing agree¬ 
ment with the doctrine of Aristoxenus, and some directly 
contradicting it: 

Gaudentius the Philosopher, a musician of uncertain 
date, though he certainly was not earlier than the second 
century, A. d. His ‘ Introduction to Harmonic ’ is an eclectic 
work combining views of the Aristoxenean, Peripatetic, and 
Pythagorean schools : 

Alypius, of uncertain date, whose ‘ Introduction ’ exhibits 
the complete scales of the three genera in all the modes, 
with their notation: 

Aristides Quintilianus, a musician of the first century, a.d., 
author of a treatise in three books on Music, in which the 
theory of the Aristoxenean school is presented in detail: 

Anonymi Scriptio de Musica (referred to in this volume as 
Anonymus) a cento of the works of Aristoxenus, Aristides 
Quintilianus, Alypius, Ptolemy, &c., probably of very late 

The works of Nicomachus, Bacchius, Gaudentius, Aly¬ 
pius, and Aristides Quintilianus, and the Isagoge are 
comprised in the Antiquae musicae auctores septem of 
Meibom. The same works, with the exception of Aristides 
Quintilianus, have been edited by Karl v. Jan in the Teubner 
edition of the classics under the title Musici Scriptores 
Graeci. The Anonymi Scriptio was edited by Bellermann, 
and published at Berlin in 1841. 




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• •••••••• 

Tovy pL€V ovv epLTTpocrOcv (^pLpiivovs rrjs appLovLKrjs Trpa- 
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De variis Titulorum lectionibus vid. Intr. B § 3 7 rap vpt&rap 

0 €a)fyriTiK‘fi Westphal : Trp^rrj rap OcapririKap codd. 8 rSpap^ rap 

Mx 9 Traph TOV R : Trap* avrov tov V B S : irap* avTov Ma, sed add. 
TOV Mx 14 TO add. Mx : t^p (o suprascr.) B 17 ^fifiipovs 

• . . aXridas restituit Westphal ex Procli Comm, in Plat, Timaeum (ed. 
Basil. 1534) P« 2 20 t-)^(ap Ma: con*. Mb 21 ovroTy] 

avrrjs S ipop/noplap Marquard: apfiopiKap H : ap/xopioop reli. 




ii&To^Vy biaroviov 6’ rj xpcofjLarLK&v ovbds ttcotto^’ k(ipaK€V. | 

15 Kai TOL ra btaypdpLpLard y avT&v ibrjkov rr/z; Tidcrav rrjs 
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3 ovb^ fipi\\pL€vovs €VpT]cropL€v avT0V9 T&v 8 ’ ovx lKav(09. 0 ) 0 * 0 ’ 15 
a/xa rooro' re (pavepov ecrrat Kal rbv tvttov fcaro\/ro/xe 0 a rrjs 
7rpaypLaT€La9 ijns Tror’ iarCv. 

5 ITpcSroi; /xez; oSz; airdvrodv Trjv Trjs (pcovrjs Kivr\(Tiv 
biopiariov rS /uteAAoz^rt TTpaypLarev^crOaL Trept /xeAovj avr^v 
TTjv Kara tottov* ov yap etj rpoTroj avrrjs ^v rvyydv^i' 20 
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I hiiropop d€ ^ xp^M^'^^Khp corr. ex -cop Sk tj •k&p S 2 S 

3 ipapfxopioop Marquard : apfAopiKap H : apfjLOPiap rell. 4 cKcycp R 
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23 ^pcffTip B R : iorrlp rell. ^ B 


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9 avrrjs seclusi : avras Westphal : avrrjs ante 5 ia<popas ponit H 

10 $6 om. S II 5’ om. B 12 rjvrivovv Ma VbB R, S linea 

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I fear a vvKvwaiv B r^iv irphs^ “tTphs r^v H 2 rlvfcv conieci: 

om. H : Toiv rell. 4 ij/iois AVestphal: Movs codd. Sri addidi 

6 Trepl 56 tov ante KadSXov, $)s post add. Marquard ovdcA 

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I avr^v Meibom : avr^v codd, 2 ^<p* kKaripas B in marg. 

5 eV] € in ras. Me : ^tt* V B R 6 Kar avrhs B R, Me (fcor parvis 
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I Toiavrrjv corn ex r^v S 2 rb 5* karavai . . . ^koko/ulcp om. M, 

in marg. Me Vb 3 ftei' post ocry add. H post •yo/) add. B R 

5 TTOiiiffosfi^v BR IO d€<rTd<r€is R ii avrds Bellermann, 

duce Anonymo (p. 49, sect. 36) : avr^v codd. ipd^yyofikvriv^ Aeyo- 
fi 4 p 7 )v B in marg. 14 ipapy €7 B 19 &p€<ns Kiv 7 j(rls iariv e/c 

TOV o^vTcpov H 20 yivofiivov B R post ^mraa^ois add. airork- 

B 21 i\a<pp6T^pov H : iKatpporkpois rell.: iXaipporkpas Mar- 
quard 22 post rerrapa add. ydp M V o 23 TroAAoi] tt in ras. M 
24 ante 6^vt7)ti add. H TavThv'\ ravrh (post h una litt. eras.) M 
ry ante Papvrrjri add. H 



5 avT&v» Act §€ TT^LpacrOaL Karavoeiv €ty avro d7rojSX€|7roz;ra5 

T&v ypphSiV kK&(TTr]v avi&pL^v ^ iinTeCvcopLev. Arjkov be tols 
ye /xr) Travrek&s aireCpoLS opyAvcov, on eirLTeivovre^ [lev els | 

10 d^VTTjra rrjv xopb^v {ayofiev avievres 8’ els ^apvrrjTa^ #ca0’ 5 
oz; be ^yopAv re Kal pLeraKLvovpiev els o^vrrjra Trjv 

Xopbrjv, ovK evbex^TaC irov ijbrj elvau rrjv ye pLeXkovo-av ecre- 
crOai d^vTTjra bta rfjs e^niracreois* Tore yap ecrrai o^rrjy orav 
rrjs emracreods ayayovirqs els rrjv upocrriKOvcrav raaiv (rrrj r\ | 

15 X^P^V pLrjKen KLvrjrau tovto 8’ ecrrat rrjs eTrirdaecos d'n'qK- 10 
kaypLevTjs Kal pLTjKen ov(Tr\Sy ov yap evbex^Tat KLveLaOaL &pLa 
20 T 7 ]v x^P^V^ Kal ecrrdvaiy i]v 8’ r\ piev k'niracris | Ktvovpevris rrjs 
Xop8^y, Tj 8’ d^TTjs ripepov(T 7 ]s rjbrj Kal earriKvCas. Tavra be 
epovpev Kal Trepl rrjs dveae^s re Kal ^apvTrjTos TrXrjz; em rov 
25 evavTLOv tottov* Arjkov be bia r&v elprjpevcov, on rj r’ &ve~ 15 
(TLS rrjs PapVTTjTos erepov ri ecrriVy o)s to ttolovv tov ttolov- 
pevovy rj T ei:ITacrIS Trjs o^rrjroy tov avrov Tporrov. "'Otl 
30 pev ovv eTepa dkkrikcov | eaTlv eiriTacns pev o^vrrjroy avecris 
be ^apvT 7 ]Tos ax^bov brjkov eK t&v elpripeviovy otl be Kal to 
T pLTov b brj Tacriv ovopd^opev eTepov ecTTiv eKaaTov t&v eipr]- 20 
12 pevcovy 11 TTetpaTeov KaTavorjaaL. pev ovv ^ovkopeOa keyeiv 
5 (fxovrjs. TapaTTeTOi)(rav 8’ fjpas al t&v els | KivTicreis 

dyoVTcov Tovs (jrOoyyovs bo^at Kal KaOokov Trjv (fxovriv KLvrio'Lv 
eivat (l>a(TK 6 vT(jdVy &s avpirecrovpevov keyeiv rjpiv otl crvp- 25 

5 &yoix€v • . . xp6vov restituit Marquard 5, 6 d^TjTTjra r^v 
^yofiiv re Kal fieraKivov/iep eis om, Ma R : in marg. add. M b: sed 
perfod. Me: praeterea el 8* els ex els Mx: el 8* els V S, B in marg. 
7 Kal ante ovk add. R ye om. B 9 ttjs om. R ayayovo’Tjs 

Marquard : ayovarjs codd. 10 Kive7rai B S 13 ante tovto 

lac. 5 litt. M : TOVTO M V B S 14 rov ivavriov tcJttov B : tov 

ivavrlov rSirov R: rcov ivavrlwv rSirrav rell. 17 Kal fi eirirarris H 

19 8rj\ov post elprjfievrov ponit H 20 rplrov] irefiirrov Westphal 

22 Kal rrrdms^ I rrr Vb e corr. 23 raparrercorrav^ errarrav in ras. 

Mb ras ante Kiviirreis add. B R 




firjcr^TaC Trore rfj KLinjcreL [xri KLveicrOaL aX)C ripeixeiv T€ Kal 
ecrravau | Ata<^€p€t yap ovbev ^pXv to X 4 y€Lv dpLaXorrjra lo 
KLvrio‘€(ji )9 fj ravTOTqra rr)z; racnv ^ €t aXXo ri tovtcov €vpL- 
CKOLTO yv(i)pLpL(OT€pov ovopLa. ovb^v yap ^ttov ripL^'is t 6 t€ 

5 <^7j(ro/x€z; kardvaL Trjv (p(o\injv, orav ripXv rj ataOTjaLS avrriv 15 
d 7 ro(l)rjvr] pJ\T kiii to o^v pirjT im to ^apv oppL&craVy ovb\v 
aXko 7 roLovvT€S TrXrjv tQ rotovro) 7ra0€t rrjy <p(ovr ]9 tovto to 
ovopia TiOepLevoL. ^aiveTai b\ tovto j ttol^lv iv tQ pL^Xcpb^LV 20 
Tj <p(ovrj' KLV€LTaL pi€V yap €v T(i bidcrTqpid tl noieivy torarat 
10 8’ Iv r5 (pOoyycp. Et be KLveLTat p.ev rr)z; fjpi&v keyopLevrjv 
KLVTjo-LVy eKeLVTjs Ttjs KiVT^aecos Trjs v'n eKeivcov \eyopLe\v 7 i 9 25 
TTiv Kara Tdxo 9 bia(^opdv XapL^avovorjSy ripepiei be TtdXiv av 
TTjv vcj)^ ripL&v X^yopLevTjv ripepiCaVy ordvTos tov Taxovs Kal 
Xaj^ovTos pitav Ttva Kal t^v avTrjv aycoyTjz;, ovbev av fipuv 
15 bia(^epoi. I crx^bov yap bfjXov ecTTiv otl fjpieLS Xeyopiev Kivr}(rCv 30 
Te Kal TjpepLLav (fxovrjs [Kal] o eKeivoi Kivr](Tiv. TaCra {lev 
ovv evTavOa iKav&s, iv aXXoL 9 be eTTLTrXeLov Te Kal (ra(l)e- 
cTTepov biiapicTTai. be \ \ Tacris otl piev ovt emTacns ovt 13 
avecTLS ecTTL iravTeX&s brjXoVy — t^v piev yap elvai (l)apLev 
20 ripepLLav (fxovrjsy ray 8’ ev tols epLTrpoaOev evpopiev ovaas 
KL\vri(reLS TLvdsy —otl be Kal t&v XoLTr&Vy Trjs l 3 apvT 7 ]T 09 Kal 5 
r?jy o^vTTjToSy eTepov ecrTLV fj TacrLS TreLpaTeov KaTavorjaaL, 
"'Otl piev obv 'qpepLe'iv (rv/xjSatz;€t r^ (fxovfi Kal eh ^apvT 7 \Ta 
Kal eh o^vTTiTa | d(l)LKopLevrjy brjXov eK t&v epiTTpoaOev otl 10 
25 be Kal Tr ]9 Tdcrecos rjpepLLas tlvos TeOeLorjs ovbev pi^XXov 
eKeivoDV eKaTepa tovtov TacrLS eorivy eK t&v pYjOrjcropLevcov 

3 om. R €vpi(rKoi rb B R 5 avr^v S : avrh R : avr^i 

rell. 7 TTOiovvT^s ex TTOiovvTOLS Mx TOVTO Th 6 vofjLa Tidcfi. ex 

TotJrw TO) (ut vid.) 6 p 6 fiaTi dcfi, Mb 9 yap om. H BiaaT'^fiaTi S 
12 T^p^ TTjs M post ijpcfic? ras. M aS t^p ex avr^p Mb : aS 
om. H 15 *6ti conieci: S 6* codd. fi/xeTs ex IfjLeTs Vb 16 Kal 
seclusi 18 fi ex t^p (ut vid.) in ras. Mb Se Bellermann : re 

codd. t6,<ti5 ex t6,<tip Mb 23 ^lp in ras. Mx 

24 a<l>iK0fi€P7i Vb^ axpiKo in ras. Mx : axpiKPovfxcprj Ysl B S : a<piKovfi€P7j R 
26 l/caT6/)^ conieci: l/carepou/ codd. 




ig ((TTai <l>av€p6v. Aei KarafxavO&vnv \ on to fiev kcrrAvaL 
t^v <l><ovr]v TO fj,eveiv im /xias Tacreds iarTi. (rvfjL^rja-eTai 
avTrj TovTOy €av r €7rt pafyvrriTos €av r €7r o^vrrjros 
IcrrrjraL. Et 8’ fj fxev rdcns iv d/x</)or€poty virdp^ei — koX 
20 ydp € 7 rt I T&v l^apecov Kal im r&v 6^e(ov to XcrracrOai r^v 5 
(fxovriv dvayKoiov , 17 8’ /xrj8€7ror€ rfj (iapvTriTL 

(rvvv'7rdp^€L )utrj8’ 17 ^apvrrjs rfi o^vrrjrt, brjkov d)9 €T€p6v 
25 iartv kKarepov tovtcov fj rdcLS d)9 | [/xrj8€z;] kolvov yiyvo- 
pL€Vov iv dpL(l)OTepoLS. *^Ort piev ovv TrevT€ ravr iorlv 
dXXrjkayv erepa, rdcLS T€ Kal Kal ^q.pvTr]s irpos bk 10 

30 TOVTOL9 dv^cris T€ Kal iirLTaaLSy ay^ebov bv^ov €#c r&v | €tprj- 

Tovtcov 8’ dvTOi)v yvoapipLcov kyopi^vov dv etrj bLeKOeXv Trepl 
rrjs Tov l^apkos t€ kqI Q^kos biacrrdcr^cosy Trorepov 

14 an^ipos icf) kKdrepd Icttiv ^ 7r€||7r€pao’/x€z;rj. *^Ort /X€z; ovv 15 
€?y y€ rrjz; <^a)z;rjz; rtOepLievri ovk kcrriv direLpos, ov yaX^TTov 
crvvibe'iv. CLTrdarjs yap <^coz;^y opyavLKrjs re Kal dv 6 p(o 7 nK 7 js 

5 d)pL\(rpL€Vos kari tls tottoj ov bL€^kpy€TaL pL^kcfbovcra o T€ 
pikyLCTTos Kal 6 kXdyLoros* ovt€ yap km to pikya bvvaTai 

fj (jxov^ €ty airetpov av^€LV Trjv tov ^apkos t€ Kal o^kos 20 
10 bLdcTaaLV ovt kiii | to pnKpov (rvvdyeLVy dAA’ XcTTaTai ttot^ 
kcf)^ kKdTepa, AtopLCTTkov ovv kKdT€pov avT&v irpbs bvo 
TTOLovpikvovs T^v dvaipopdv, TTpos T€ TO (pdeyyopLevov Kal to 

15 Kpivov TavTa 8’ kcrTlv rj T€ <p(»)v^ Kal 17 | aKOTj. b yap 
dbvvaTovcriv avTai fj pikv TroLeiv fj be KpiveiVy tovt e^o) 25 

2 fjikWov B 3 €7r’ in ras,, erat ott* Ma 4 ’IffTtiTai MBS: 

iarrirai Me Vb R ci tj fihv] tj dk sed ras. post $6 M : r) d* ci fiiv 
Vb: § 5 * 64 fjL€v B in marg. : rj d' fj fihv S 8 fjirfiiv del. Marquard, 

recte 14 Siao’Tao’ecus M (?) B : ^lariff^oDS V S R, B in marg. 

15 cKarepd Meibom: cKorepas codd. fj ex rj Mb : ^ B 16 ye 

conieci: om. H : re rell. 18 rdiros Meursius : t6vos codd. 

20 ^ ante els add. S 21 dido’raa’iv^ <r ante t eras. M : didraffiv 

rell. '[(TTaadal B R 23 dia<popdt/ R irphs post Kal add. H 

24 5’ om. B 25 ttolcTv] €11/ in ras. Mb Ifw Bellermann : 





deT€ov rrjy t€ \prr\(Tiiiov koX bwarfjs iv (jxovfj y^vicrdai 8ia- 
(rra(r€a)y. ’Etti ii\v ovv to fjLLKpov afxa irods €OLKa(nv rj re 
(jxov^ Kal I Tj aicrOricris i^abvvar^lv ovt€ yap rj (pcovr) 8i€- 20 
<r€a)y rrjs ikaxiorrjs lAarroj; in hiafTTqpia hvvarai biacaipeLV 
5 ovb^ 7) CLKO^ biaLcrOdvecrOaL (Sore Kal ^vvUvai tl fxepos icrrl 
bUo-ecos €LT aXXov tlvos t&v yvcapifjLcov Staarrj/xarcoz;. | ^Kirl 25 
§€ TO fxeya rax" b6^€L€V v7r€pT€LV€LV fj aKorj rrjv (f)(ovriv 
ov pievTOL y€ ttoAAS tlvl. ’AAA’ obv etr €7r’ dpL(f>6T€pa bet 
ravTov XapL^dveiv | irepas Trjs bLaardaecos, eU re rriv (jxovrfv 30 
10 Kal TTfv aKor}V fiXeTTOvras, €?r’ eirl piev to eXdyLcrrov TavTov 
€7rl be TO p,eyi(TTov eTepov earat tl pLeyicTov Kal eXdyjLorov 
pLeyeOos lijs bLaoTd\\(rea>9 ?/rot kolvov tov (f>6eyyopLevov Kal 15 
Tov KpivovTos rj ibiov eKaTepov. *^Ort piev ovv els Te Tr}v 
(fxovrjv Kal Trjv CLKorjv TeOelaa ij tov ^apeos Te kcu o^eos 
15 bL\d(rTao‘LS ovk eis aireipov 6<^’ eKdTepa KivrjOricreTaLy a^ebov 5 
brjXov. ei 8’ avTT] #ca0’ avTrjv vorjOeCr] 7} tov pieXovs otJ- 
cTTaais, T^v jav^cTLV eis aTretpov yLyvecrOai {el) (rvpL^ricreTai 
Td\ av dXXos elr] irepl tovtiov | Xoyos, ovk dvayKoios eis to 10 
TTapoVy bidirep ev tols eTreiTa tovt eiTLaKexIfacrOaL iretpaTeov. 

20 Tovrov 8’ ovTos yvcopipov XeKTeov Trepl (f>96 yyov tl 
TTOT ecTTL. | 'SiVVTopLLos piev OVV el'neiv (fxovrjs ttt&o-ls em pitav 15 
Tdcriv 6 (l)66yyos eort* rore yap (patveTat (pOoyyos elvai 
TOLovTos OIOS els p^Xos TdTTeaOaL | Tippoapevov, {oTav rj 20 
<f)(ovri (pavfj) ecTTdvat em /xtay Tdaecos. pev ovv (pOoyyos 
25 TOLOVTOS eoTLV* bLd(TTr]pa 8’ ecTTl TO virb bvo (f)66y\y(ov 25 
d)pL(rpevov /xr) rrjz; avTTjv TdcrLV eyovTOiv. ^au;€rat yap, d>s 

I diaffraffcoos M (<r ante t eras.), S, B in marg. : diarda^as R, Vb 
fort, e corn, B 5 ^ om. B 6 efre ante parvis litt. 

supra lin. add. Me, in marg. B, R : om. rell. 9 Biaria’cas B S R 

12 diacrdo'eas^ <r ante t eras. M : Siarcurecus B R 13 ef (<r 

suprascr.) re B 15 eis] in H 16 yoTjdclTj] dxSciT) H 17 et 
restituit Bellermann 22 6 om. H opos <l>d 6 yyov add. in marg. 

Mb Vc iffri Tore ydp (paivcrai (pddyyos add. in marg. Ma 23 oraif 
TJ <p(av^ <po.v^ restituit Meibom 25 *6pos ^latrrijjiaros add. in marg. 




rvTTw elTTelv, dcatpopd tls elvai Td(r€<av to didarrrjfjLa Kal 
TOTTos beKTLKos (f) 66 yy(ov o^vripcAV pL^v rrjs ^apvrepas r&v | 

30 opi^ovaQv TO btdcTTTfpLa racrecoi;, fiapvT€p(av be t ^9 d^vTepas* 
bLa(l>opa be iarl Tdcrecav to p.dkXov ^ ^ttov TeTdcrOau Uepl 
[lev ovv 6ta<rT7//iaroy ovt<o 9 av tl 9 d<f>opla‘eie* to be <ri;- 5 

16 (TTrjfia (TvvOeTov rt || vorjTeov eK irkeiovoiiv rj evbs 8ia<rrrj- 
fidTcav. Aei 8 ’ eKaarov tovt(»>v ev ttcoj eKkapifidveLv 
TreLpdo-dat top aKOVOVTa /xrj TrapaTripovvTa tov dirobibopLevov 

5 koyov I IfcaoTOV avT&v eiT earlv aKpL^^s eire Kai tuttco- 
becTTepoSy dkk^ avTov (TvpLTrpoOviioviievov KaTavorjaai Kal 10 
TOTe olopievov Ikov&s eiprjaOai irpos to KaTa/iadeiv, oTav 
10 efXjSijSaorot oloy re yevYjTat 6 | Xoyoy els to crwievaL to 
keyopLevov. ^akeTrbv yap virep irdvrcav pXv tao^s t&v ev 
dpxfi koyov dveTTikrjTTTov re Kal bvf]Kpi^o>[ievr\v epiiriveiav 
15 expvTa prjOrjvai, ov^ ^Kto-Ta be Trepi TpL&v TOVTOiVy | (f> 96 yyov 15 
re Kal biaor^piaTos Kal avcTTripLaTos. 

Toi/rcoz; 8’ ovrcay ^picrfievoiv irp&Tov fiev to bidarTTjfia 
20 TreipaTeov 8te|Xetz; eh bcras Trecj^uKe btaipeaeis biaipelaQai 
Xpr](TipiovSy eTretra ro avo-Ttjpa. IT/xorij piev ovv ecrrl 
8ta(rrrj/xara>i; bLaipeaLs Kad^ rjv pieyeOei dkkijkcov bLa(l>epeL* | 20 
25 bevTepa be KaO^ fjv ra oiipLcfxava t&v bLacfxovcov* TpiTrj be 
KaO^ ^v ra avvOeTa t&v dovvOeTcov* TeTdpTrj 8’ fj kotcl 
30 yevos* I 'TTepLTTTYj be Ka0’ rjv bLa(l)epeL ra prjra t&v akoyodv. 
Tas be koiiras t&v biaipeaeoav &s ov xpr[(Ti[iovs ovaas eh 

17 TavTrjv TTjv TrpayfiaTeLav a^ereW ra vvv. j| ^vaTYjjia 8 e 25 

3 6 pi^ 6 vT(ay R t6 re R ii ol 6 jii€i/oi S eipeitrOai 

S 12 iKpifidtrai R ycyrjrai] rirou in ras. Mb Xeyijiicvoi/^ 

rh : post h ras. M 13 ante /liv una litt. eras. M jxhv] ^Ivai B R 
Tay\ rh R : rhi/ V B S twi' . • • ^Kiffra S€ om. H 14 Xdyoav M 
15 ^Qirfyiav R 16 ciKTr^/ioros] Biaa’rdifjLaros B R 18 di€\€ii/ V S 
sed €11' Vb in ras.: BicKB^Tv M diaip€<r€is om. B sed in marg. add. 

19 H €7r€£To in ras. Vb: /col eri in ras. Ma 

20 iioup€(r€is diaardifiaros deinde numeri d. jS. /ctI. in marg. Mb 

Vc 23 dia<l>€p€i om. H \ 6 yoi)y B R : ^rjr^L tmv a\ 6 y(av in 

ras. Mb 



avorrifiaTos ravraLS re StotVet raty {avrats) biatpopais ttA^z/ 
/xtay—^fxeyeflet re yap brjKov &9 biaipepeL (rvonjl/xaroy av- 5 
oTTjpa Kal T& [re] (rvp(p(ovov9 rj biapdvovs ^Ivai roivs opi^ovra^ 
<f)66yyovs to /xeyefloy. r^z; 8e rpCrriv r&v prjOeLc&v eTrl 
5 T&v Tov buKrTTiparos bia(pop&v abvvarov v'nap^ai | crvon^- lo 
pan Trpos (rvarripa, brjkov yap &9 ovk ivb^xeraL ra p€V 
(TuvOera ra 8’ aoiHvO^ra nvai r&v avo-rripdrayv tovtov ye 
TOV TpoTTov ovirep T&v btaoTTipaTcov ra pev ^v (ruvd^Ta ra 
8’ dcrvvO^Ta. t^v | 8e T^Taprqv—avTrj 8’ ^v rj Kara yevos 15 
10 —dvayKoiov kolL tol 9 (ruorrjpxLo-LV VTrdpxetv, ra pev yap 
avT&v e(rrt btdTova ra 8e ™ ivappdvLa. 

bijXov 8’ OTL Kal (rrjz;) Tre/xTT'n/z;, ra /xez/ | yap avT&v dAoyw 20 
btao-TT^paTL c3pt(rrat ra 8e py]T&. Upos 8e ravraty rpety 
erepay -Trpoo-flereoz; 8tatpe(rety r^z; r’ ety avvap^v Kal bid- 
15 C^v^LV Kal TO avvapcpoT^pov p^pi^ovaav ra (TVcrTripaTa* | 
(tt&z; yap (rvorripo) dird tlvos /xeyeflovy dp^dpevov rj (rvvrjp- 25 
pivov ^ bteC^xr/pevov rj ptKTov e£ dpcpoTepoiv yiyv^Tai (Kal 
b^LKVVTaL TOVTO ytyvopevov kv kviois)* eTretra t^z; r’ ety 
VTrepjSaroz; Kal (rweyks p^piQiv\(Tav, irdv yap (Tvarrjpa r/rot 30 
20 ovv€X€9 7j virepfiaTov ecrrt, rzjz; r’ ety aTrAoCz; Kal btTrkovv 
Kal TToXXaTrkovv biaip^criVy ttclv || yap to kapfiavopevov l8 
(ru(TTr]pa ^rot a/nXovv rf biTtkovv rj iroWaTTkovv kortv. Tt 
8’ earl tovtcov eKaorov kv toXs eTretra beixOrjaeTau | 

Tovtoov 8’ ovTOi)s dcjxopLcrpkvcov re Kal TrpobLjiprjpkvoov 5 

I (TvffT^ifjLaros ^iaip4<r€is Mb Vc in marg. ut supra avraTs restituit 

Westphal : ante raTs ras. in qua erat rats av M 2 r€ in ras. in 

qua erat re drj Ma: Se B yitp H : om. rell. 3 /cal in ras. Ma : 

om. rell. re seclusit Marquard 4 de in ras. Mb: piivToi BR 

5 diao’T'fifjLaros Vb B S : <Tv<TTi)fiaros MR 7 5 ' affvvB^ra om. R 

^Jvai . . . 5 ’ affvvB^ra om. S g rh post Karh add. H 12 r^v 

restituit Marquard 13 pyjr^. Uphs dc om. B, sed in marg. add. 

14 kripas ante rp^is ponit H eis in ras. Mb 16 irav yap 

o’va’TtifjLa restituit Marquard ^7 ^ di€(€vy/j.€i/ov ante fj (rvvrjixfxcvoi/ 

ponunt codd.: ordinem restituit Marquard 18 re post eis ponit 

H: r in marg. Mb 20 koX dnr\ovv om. R : f in marg. Mb 

22 ^ BittXovv om. B 23 Sex^^ercToi S 




TTepl ixekovs &v etri fjpLLV 'n^tpariov VTTorvTr&craL rt ttot 
icrrlv fj (f)V(TLS avrov. "Ort piev ovv bLaarrjpLarLKTjv iv avT& 
lo b€L TYjv rfjs (poi)\vrj9 Kivr](Tiv ^Xvai TTpoeCpriTaLy (Sore rod ye 
AoycSSouy #c€)((opi(rrat ravrri to plovctlkov /xeAos* Aeyerat 
yap bri #cal Xoyiobh tl iM€\oSy to crvyKetpLevov €#c t&v Trpocria- 5 
15 bi&v T&V iv TOLS dvopLaCTLV I <\)V(JLKOV yap to iTnT€LV€lV Kal 
avUvai iv r£ btakiyecrOau ’ETret 8’ ov \k6vqv €#c Staorrj- 
IxaTwv T€ Kal (l)66yy(i)v crw^ordvai bet ro fjppLoapLivov /xeAos, 

20 dAAa TTpocrb^iTaL crvvOicreds tlvos Trotds | Kal ov ttjs tv^ov- 
(TTjs—bfjKov yap g>s to y €#c biacrTTipATcov re k 6 X (pOoyycov 10 
crw^cTTavai koivov icrTiv, virapy^i yap Kal r 5 dvapfiocrTK ^—, 
dSoT* eTretSrj tovB* ovtoos to p^iyiaTov piipos Kal TrAetorr/z; 

25 I i^ov poTTTiv et 9 Trjv 6p65>s yLyvop.iv7]V crvcrTacnv tov piikovs 
(ro) Trept rr/r avvO^aiv KaOokov Kal Trjv TavTTjs ibtoTrjTa 
VTrokTjTrTiov elvat. 8rj (pavepov, otl tov /xez; im 15 

30 Trjs Ae£ea )9 yi\yvopiivov piikovs r 5 8 ta(rrrj/xartfc^ )(p^(r 0 at r^ 
Trjs (fxovrjs Kivri<r€L StotVet ro plovctlkov juteAos, roi) 8 ’ dvap- 
pLoaTov Kal bLTjpLapTTfpLivov TTf TTjs cTwOccTcoiS biacpopa Trjs 
19 Toiv darvvd€T(ov 11 biacTTripLaTcoVy irepl iv rots eVetra 
bcLxOw^'^^^ rts icTTLV avTijs 6 rpoTroy. TrkrfV iirl toctovtov 20 
5 y’ clp^crOo} KaOokov Kal vvvy otl rrokkas ixovTos bLa\(f)opas 
tov rippLoapLcvov KaTa ttjv t 5 >v bLacrTTjpLaTcov crvvOccTLVy opLoos 
eVrt TL TOLOVTov o KaTa iravTos fippLoapLcvov prjOrjcrcTaL iv 
re Kal TavToVy TOLavTTjv ix^^ bvvapLLV otav avTrfv dvaLpov- 
10 piivrjv I dvaLpeiv to rjppLoapiivov. airkovv 8’ icTTaL TTpoiovcrris 25 

I TTcpl ficKovs in marg. Mb Vc iirirvTrao’cu R 2 ^KrrrjfiaTiK^p 
B 3 ye] y S 4 \4yeTai • . . ficKos om. B sed in marg. add. 

5 5 ^] t\ S 6 Twp €P rots Meursius : rh ip rois codd. 7 iircl 

5’ BR : ^TTcira rell. 8 <Tvpi<nivai B 9 rvxns R ^3 opBas 
. . . TTcpl T^p parvis litt. supra lin. Me, in marg. Vb 14 rh restituit 
Marquard Kad6\ov conieci: Kiirou H : Kai ttov rell. /cal seclusit 
Bellermann 15 i^rl rrjs Aefews Bellermann, duce Anonymo 

(P* 55) • iTTiTTidcicps codd. 16 diao’TTjfiariKfi xpriffQai Meibom : 

5 io<rT^/iOTi K€xpV<TBai codd. 18 BiafjLapTrjfiipov B 20 6 om. H 
21 clpcio’da S 24 ravrSp^ ravrh (post h litt. eras.) M : Tavrhp V : 
Tavrh rell. apaipovfiiprip om. B 



rrjs 7rpay/xar€tas. To /x€z; ovv fiovcrtKov fiekos airb r&v 
aX\(i)V ovT (09 acfxopLcrOa). V7roXr]7rT€ov §€ rbv €lpr]fi€vov 
CLipopLcrpLov TVTTia €l\p7j(r9aL ovTcos ws pLTjbeTTd) T&v #ca0’ eKacrra 15 

5 ^F,)( 6 pL€Vov 8’ av etrj rcov elpTjpLevayv to KaOoXov k^yopL^vov 
piekos bL€k€LV €ts oca (f)a(v€TaL yiv 7 \ bLaLpeLO’Oau <I>at- 
v€TaL I 8’ €ts Tp(a* TTCLv ycLp ro kapL^av 6 pL€Vov pinkos rdv 20 
€ts ravTo fippLoapLevcov ^tol biarovov kcrriv rf yjxopLarLKov ^ 
ivappLovLov. Up&Tov pLev ovv Kal Tip^cr^vTaTov avr&v 6€T€0 v 
10 ro bidrovoVy Trp&rov yap | avrov fj rod dvOp^TTOv (pvas Trpoa- 25 
Tvyxdvety bevrepov be to yjxopiaTLKoVy TpiTov be #cat dz;(o- 
TaTov TO evappLovLoVy TekevTaCio yap avTQ Kal piokis /xerd 
TTokkov TTovov (TvveOi^eTai fj ataOrjCnsi I 

Tovrcoz; 8’ els tovtov top dptOpibv bijipripLevcov t&v bia- 30 
15 aTTipiaTLK&v biaipop&v Trjs bevTepas prjOeLcrrjs OaTepov piepos 
TreLpaTeov biaorKeij/aorOaL —.tjz; be rd pLeprj TavTa biacfxovLa re 
Kal II (TvpLipcovLa—kTjTrreov re rrjz; crvpLcIxoVLav els Trjv eTrt- 20 
(TKey^nv. ^aiveTai be bid(TTr\pLa avpLcIxovov (rvpLcfxovov bia- 
(l)epeLV fcard irkeiovs biatpopas &v piCa | piev ecrTLv fj #card 5 
20 pieyeOoSy Trepl rjs dtpoptaTeov p (paLveTat eyeiv. Aofcet 8e 
ro p.ev ekd\i(TTov tS>v avpicpioviov dtao-rrj/xdrcoz; vtt avTrjs 
Trjs Tov piekovs (pvcrem dcpcopLo-OaLy pLekcobelTat piev yap | 
roi; 8td Tecradpayv ekaTTO) biacrTripiaTa rrokkdy bidcpcova piev- 10 
rot TrdvTa, To piev ovv ekdyicTTov KaT avT^v ttjv rr/s (pcovfjs 

2 a<po)pi<TQo) ex aiputpi^lado) Ma Thv\ M (corn Me) 3 ei- 

prj<rdai ex clp^fiada Me : cipcTo’dai S ^KaffTov R 6 els om. S 

8 ravrh eonieei: rh eodd. rjpfio(rix 4 va)v eonieei: ^pfjLOfffiivov eodd. 

^pfiofffjiivov Marquard lo yh.p Marquard : re eodd, 

apdpdavov^ etpov S Trpo<Trvyxo>v^^ Vb R S: fell. 

II pc^rarop H 12 ipapfxopiop ex t^p apfioplap Mb 14 5 i- 

“pprificpop B 16 a’Kc^ao’dai R Ka^ ffp rh <r^fjL<pa)Pa rap 

^ia(p<&pa>p dia<l)€p€i in marg. add. Mb Ve 17 Xtjvtcop rel re om. B : 

56 S 22 aipuipiffQai ex a<pa)pi€i(r 6 ai Mb : o’ in ras. Vb fxlp 

om. H 24 rh om. B : supra lin. add. Mb rijp om, B : supra 

lin. add. Mb 


1 . 20 


^vcriv wpLcrraty to be \ieyi(TTov ovt(o fxev [ovv] ovk eoiKev 
15 6pi\^e(T0ai* (^aiverai yap eh aiteipov av^ecrOai Kara y avrrjv 
T^v Tov piekovs (^vcriv KaOdirep Kal to bLdcjxovov. iravTos 
yap TTpocrTLOepLevov avpiclxovov StaoTTj/xaros Ttpos t& bid 

20 iracr&v | Kal pieCCovos Kal eXdTTovos Kal tcrov to oXov yiyve- 5 
rat (TvpLcIxovov. OijTO) piev ovv ovk eoiKev eXvai tl p,eyi(TTov 
(rvpLcjxovov 8ta<rrrj/xa* #cara p^evToi ttjv rjpLeTepav xp^o'iv — 

25 Xeyo) 8 ’ fjpieTepav | rrjv Te bid Trjs dvOpdirov (pcovfjs yiyvo- 
pievrjv Kal t^v bid t&v 6pydv(ov—^aiveTai tl p^eyiaTov ehaL 
T&v oDpLcjxovcov. TovTo 8 ’ icTTl TO bid TTevTe Kal ro 8 ts 8 ta lo 
30 Tracr&Vy TO ydp Tpls bid | 'naa&v ovk eTi biaTeLVopLev. Ael 
be T7]V bidcTTacriv opi^eiv evos tlvos opydvov tottco Kal 7re- 
paatv. Tdxa ydp 6 t&v TrapOevCcov avX&v o^vTaTos (fyOoyyos 
irpos TOV T&v vTTepTeXeLoov (iapvTaTov pLet^ov dv TToiTjcreLe 

21 TOV elpTjpievov Tpls bid iraa&v 11 bidaTripLa Kal KaTacrTracrOeLcrris 15 
ye Trjs avpLyyos 6 tov avpiTTovTos o^raros rrpbs tov tov av- 
XovvTos ^apvTaTov piel^ov dv TroLrja’eLe tov prjOevTos 8ta(rr?j- 

5 pLa\Tos* TavTov be Kal iraibbs (fxovri pnKpov rrpbs dvbpbs 
(l)(ov 7 iv irdOoL dv. o 6 ev Kal #caraz;o€trat ra pieydXa t&v 
(TvpLip&vcov eK btaipepovcr&v ydp fjXiKL&v Kal btatpepovTayv 20 
10 pL^Tpcov TeOecoprjKapLeVy | ort #cat ro Tpls bid rraa&v (rvpL<p(»)veL 

I fjLcyiffTOP Meibom H : fiiy^dos rell. oZv seclusit Marquard 
2 dpiuffdai MVS: apio’dai H y^Lp supra lin. Mb: di {y^p 

suprascr.) B a corr, manu: 56 R 3 didipavop ex ^ii<popov 

Mb: ^i<po)vov B 
10 toDto] tov S 
^\s ^id Traffav 
5 IT 


5 * 6 \ov’\ * 6 \o)v S : Sxiyov R 6 odp om. B 

rh 5 is] rh supra lin. B 
^id €\ 
if 5 

' in marg. MbVc ii rb y&p VbB RS : 

TOV ydp M (ydp in ras. Ma ut vid.) : /iexpt ydp tov Marquard : ydp om. H 
Upa Tlop<l)vpiop iv Ty els dpfioviKd xmofiviifiaTi add. in marg. H ovkcti ex 
odv iffTi Ma BiaTcipapLcp B 12 ^laTaffip R TSvep Westphal: 
t 6 pjp codd. 13 Trapdcviav M Vb R vapd. ovA. linea subducta S 

14 t 5 i' om. R fiapvraTov Marquard: fiapvraTosv codd. 15 tov 

R: TOVT* rell. KaTa<nrad€l<rrjs M H 17 ‘iroiiio’ete dido’TTjfia tov 

Tpls did ‘trao’av €lp7jfjL€Pov diacriifiaTos H pTjdcvTos] post ^ ras. M 
18 ^ ante iraidhs add. et <po)v^ post juiKpov ponit H 




Kal ro T€TpdKLS Kal to ^OtL fl€V OVV 6776 ll€V TO 

jlLKpbv Tj TOV pL€k 0 V 9 <pV(rL 9 OVT^ TO hlCL TecradpCOV ikaXLCTOV 
a 7 rob[boi) 0 ‘L t&v crupLcIxoviov, iirl §6 ro /X6|ya Tjj 7 iii€T€pcj. tto)? 15 
ro pt^yi(TTov 6 pL^€TaL 8wa/x66, crx^ebov brjkov 6K rc3z; eZprj- 
5 pL€VOi)V OTL 8’ dfcro) pLey^Ori oDpLcfxoviov biacrTTjpidTOiv avpifiaLveL 
yiyv^crOai pabtov a‘vvLb€LV.\ 

Tovtcov 8’ ovTOdv yvcopipLcov ro Toviaiov bid(TT 7 ]pLa 7766- 20 
paT€OV d(l)op((raL. "'Ecttl brf rdz;oy fj t&v TTpol^Tcov crvpLcIxovcov 
Kara /X6y60oy bia(^opd. ALaLpeLcrOa) 8’ 66? Tpets bLaLp€ 0 ‘€L 9 * 

10 pL^kcobeLO’Oo) yap | avroi; ro r6 ijpLLav Kal ro TpLTov piipos Kal 23 
(ro) T€TapTov TCL 86 TovTcov iXaTTova biaarripLaTa iravTa 
loTO) dpL€kcobr]Ta, KaX^CaQo) 86 ro pL€V iXd\LOTov 
kvappLovios ikaxLCTTri, ro 8’ kyopL^vov | bUcrts xpoopLaTLKri 30 
iXayLCTTr], to 86 p^iyiaTov rjpuToviov. 

15 Tovrcoz; 8’ ovt (09 dipaypLapLevcov ray t&v y^v&v buacpo- 
pas o 6€V yiyvovTai Kal ov Tpoirov 7r€LpaT€ov KaTapLaOelv. 

A66 86 11 vofjcraL t&v avpicfxovcov bLacrTrjpidTayv (ro) ikdyLO-Tov 22 
ro KaTeyppL^vov Td y6 irkeiaTa V7rb T^TTdpcov (pddyyoiv 
o 6 €V brj Kal t^v irpoariyopLav vm t&v naXai&v 6o^6 • • • j 
20 \Tiva 8rj Td^iv TTk^Lovoov ovcr&v voryriov; Iv if laa Td r6 5 
Kivovpievd elcTL Kal ra 'qpepLovvTa ev Tats t&v y€V&v btacpopa'is. 
TCyveTat 8’ iv t& tolovtco oXov ro d77o pL^aris i(f)^ virdTrjv 
iv TovT(o yap bvo piev ol 7 T€\pL€yovT€S (pOoyyoL aKLvrjTOL 10 

3 Trj TffjLcpa S 5 OKT^ Westphal: €K rav codd. ficycdci 

M V R S Kal ante ^laffTrjfjLdrav B R, parvis Ktt. in marg. Me 
7 * 6 pos t6vov add. Mb Vc in marg. 8 ^ om. S ii restituit 
Marquard $6 e corn M 15 aipopiafiivtav S 17 Se] \ in 

ras. B rh restituit Marquard 18 KarexifJ^^vov conieci: 

Ka\ovfi€vov codd. y€ conieci : om. H : t€ rell. 20 seqq. riva 

. . . Kivovvrai seclusit Westphal ut glossema 20 riva rd^iy R : 
Tiy (o suprascr.) 5 al rd^iy ( 5 ol rd in ras.) Me: rivd irpa^iv V S, B in 
marg.: rivd de rd^iv B : riva irpd^iv H post ovffSav add. x^p^c^y 

supra lin. Me, xop^&t^ cum duobus punctis praepositis, punctis in marg. 
repett. B, x<^P^^ cum cruce R, <rvyxopdiai/ Westphal 






elcTLV iv TOLS T&v y€v&v biaipopaLSy bvo 8’ ol n^pi^yopi^voi 
KlVOVVTai^ ToVTO pL€V OVV OVTOa K€L(r 6 (i). T&v b€ (Tvyxpp- 

bt&v 7r\€L6voi)v T ovcr&v r&v Trjv elprjpLevTjv ra^iv tov bia | 

15 T€(r(rdpOi)v Karexpvcr&v Kal ovofiaaLV ibtoLS Ifcaorijy avr&v 
&pL(TiJL€V 7 i 9 y Ilia ris ioTLV fj iii<Tr\s koX Xiyavov koX Ttapv'ndrqs 5 
KoX VTrdrrjs (rx^bbv yvcopifioordTr] tol9 airrofievoLS fiovcrLKrjs 
20 iv if ray | r&v y€V&v biacpopas dvayKoXov iTTLcrKiifracrOaL 
riva rpoTTOv yiyvovrau *^Ort [liv ovv al r&v KiveXcrOaL 
7 r€(pvK 6 T(ov (pOoyyayv iiurdcr^LS re Kal dvicr^LS oXriai elcrt 
25 rrjy r&v y€V&v btacpopas (pav^pov. ris 8’ | o tottos rfjs 10 
KLvri(r €(»)9 iKaripov r&v (pOoyycov tovtoov k^Kviov. Aiyavov 
piiv ovv iarl roviaios 6 crvpL'nas tottos iv w Kiv^iTaiy ovt€ 

30 yap iXaTTov dcpioTaTat piicrris Tovtaiov 8 ta(rr 77 |/xaroy ovt€ 
PL€lCov biTovov. Tovtcov bi to piiv ikaTTov irapa piiv t&v 
rjbr] KaTavevoriKOTCov to btdTOVov yivos [o^x] bpLokoyelTaty 15 
23 Trapd bi t&v /xtjtto) avvecopaKOToov avyycopoLT &v [| € 7 ra- 
xOivTcov avT&v to bi pi^iQiv ol piiv avyxpypovaLV ol 8’ ov. 
bi fjv bi yiyv€TaL tovto ahiavy iv tols €7r€tra prjflTjaerat. 
"'Otl 8’ €(rrt tls pL^koTToua buTovov Xtyavov beopiivr] Kal ov\ 

5 Tj (pavkoTdTT] ye dWa a^ebov fj fcaAAtorrj, | roty piev ttoWoIs 20 
T&v vvv dirTopLevcov pLovcnKrjs ov irdvv evbrjkov eort, yivoiTO 

I y^vSiv^ <pd 6 yya)i/ H 2 tovto ex tovtcov Me, duobus punctis 

subscr. et av suprascr. B : Toincov V S (rvyx^p^f^y H 3 Tav 

T^y] T&v B in ras. : om. R 4 ovSfiaffiv post l^lois ponit H 

5 Xlxai^os (ut constanter fere) Ma : in \ixavhs corn Me: Va semper 
\lx<iyos : yp' \ixdvov Vb in marg. 6 Kal om. V S vwaTrts 

in marg. Mc(?) toTs ex Ttjs Mb: Trjs R avrofiivTis MVR 
9 T€ om. H 10 tSvos Marquard : Tp 6 iros codd. ii cKaffTov H 
13 cupiffTorai Marquard H : d(pi<rTa<rdai rell. : cuplcTaffdai (paivcTat 
Westphal 14 ^ it 6 vov^ post i litt. a eras. t 6 renovatum 

Mb: diaTdvov ex ^it 6 vov Vb (ut vid.) : ^itovov (o super i scriptum) 

B : diarSvov S t&v t&v fj in ras. Mb 15 dlTovov H 

ovx seclusi: ovx SfioXoycTTai in ras. Mb 16 vaph^ ircpl S 

ffvyxopoiT^ B R iirax^ivTcvv av in ras. Mb 17 avrep R 

18 TOVTO post cTTciTa add. M (eras.), VS,B (suprascr.) 19 5 io- 

Tovov (duobus punctis sub. o) B ^cofiivri] ri in ras. Mb ovx 
M V S R 20 (pavXdTTjTi B y€ om. H 



jxivrhv €7ra\6€L(rLV avrois* rois he ovveLOLcrfievoLS r&v 
ap\\diK&v rpoTTcov tol9 re 'rrp<0T0LS Kal rois hevrepoLS iKav&s 10 
hrjkov ioTL TO Xeyopievov. 01 piev yap rfj vvv Karexpvcrrf 
pLekoTTouq, <ruvri 6 eL 9 piovov ovres elKorcos r^v hirovov Xiyavov 
5 i^opL^ovar | awrovcorepaLS yap xp&vrai ayehov ol irkeiaroL 15 
T&v vvv. TovTov 8’ aiTLOv ro ^ovKecrOai yXvKaiveiv aet, 
crrjpLetov 8 ’ on tovtov crToyaQ^vraiy pLoXicrra pkv yap Kal 
irkelarov xpovov iv xpiopLan hLa\TpL^ovcrLVy orav 8’ 20 
a(l)CKOi)VTa( TTore eh rrjv appLovtav, eyyv 9 rov ^(pw/xaroy 'npocr- 
10 ayovcn avveTnaTroiypLevov rov rjOovs. Hepl tovtoov piev ovv 
eirl ToaovTov apKeLTO)* 6 8^ lijs X^xavov tottos tovkuos I 
yTTOKeLO-Od), 6 he ttjs 'Trapv'TrdrTjs hLeaecos eXaxtorrjy. ovre 25 
yap eyyvrepd) rfjs virarris Trpoaepx^TaL htecrecos ovre TiXelov 
dipLararaL ripLiaeos rovov. ov yap eTraXXdrTovaLV ol roTroL, 

15 aXX^ eoTLV avr&v Trepas 17 | avvacp^q, orav yap em rrjv avr^v 30 
rdcnv dcpUiovraL rj re TrapyTrarr] Kal rj Xtxc^J^dsy rj piev € 7 rt- 
TeivopLevT] 7 j V avLepLevrjy nepas exovcrtv ol tottol* Kal ecrnv 
6 piev em to fiapy TrapyiraTriSy 6 8’ eirl ro || o^y Xtxavoy. 24 
Hepl piev ovv t&v oX(ov tottcov Xlxo^vov Te Kal TrapvTraTrjs 
20 oyT (09 &pL(r6(Oy Trepl he t&v #cara (ra) yevrj Te Kal tcls xpoay 
XeKTeov. To piev ovv 8ta Tecrcrdpodv ov Tpomv | e^eTaaTeov, 5 
eLTe pieTpetTaL tlvl t&v eXaTTovcov hLaaTrjpLaTOiyv etTe irdcrCv 
ecTTiv daypLpLeTpoVy ev Toh hta crypLcIxovLas XapifiavopievoLS 
XeyeTar &s (paivopievoy 8’ [e^] eKeivov hvo tovcov Kal 

I iTraxStjciv H a’vvcidio’fjLcvois (ei ex 7)) Mb : (rvi/ 7 }dia’iJL€vois S : 

<rvi/€di<rfi€vois H 4 fiSvov post 6 vt€s ponit H dlTovov~\ post i 

litt. eras, M sed. in marg. \ixo,vhv B 5 bpi^ovai 

R avvTovoripais S 6 aU\ B 10 fjdovs Meibom: tQvovs H : 
60OVS rell. ii 5^ Marquard : $6 codd. 14 € 7 ra\\iTTov<riv 

ex iXarrovaiv Me, Vb in marg. cum signo 7/, R : iXarrovaiv Va S B in 
marg. 18 \ixav6s B R 19 irepl . . . Aixa^'ov om. M, et Kal 

TTcpl Tovrav fihi/ add. in marg. Mb: eadem VaS,B in marg.: quae in 
textu scripta data in B R et Vb in marg. cum signo yp' 20 6>pl(rdai 
B sed Of suprascr., M sed i in ras. Mb : 6pl<rda> Va restituit 

Marquard post re ras. M 22 hiaarfviiriav om. Va S: add. Vb 
in marg. 24 ef del. Marquard 3voiv H 

I 2 




lo ^/xt|(r€oy, K^LcrOa) tovto hv etvai ro /x€y€0oy. TIvkvov be 
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ekarrov bidcrTrifia Trepte^ei rod keLTrojJiivov biaorruiaTos ev 
15 T& bia recrcrapoiv. | Tovrcoz; (8’) ovroos Sipicrpievoiv Trpoy rS 
l^apvTepco T&v pievovrcov ipOoyycov €t\ 7 j<^ 0 co ro ikd)(^L(rTov 5 
TTVKVov* TOVTO 8’ eo’TUL TO €#c 8vo bUcTeodv {evappLovCiov eXa- 
ylcTTdiV* € 7 r€LTa bevTepov Trpbs t& avT&* tovto be ecrTai ro 
€#c bvo bteaecov) yj)(»ip,aTiK&v ekayicTTOiv. ecrovTat be (at) 

20 bvo Xt|xai^ot eikripLpLevaL bvo yev&v ^apvTaTaL, rj p.ev dp- 
pLovCas fj be xp<opLaTos. KaOokov yap ^apvTaTai p!ev al lo 
25 evappLovLOL kixavol exopLevat 8’ at xpo^pLaTiKaiy (tvv\tov- 

(oTaTat 8’ at 8taroz;ot. Mera rai;ra TpiTov elk'qtpOo) ttvkvov 
TTpbs^ Tea avT&* TeTapTov (8’) elkri<p6oi) ttvkvov tovloXov* 
TTepLTTTov be TTpbs T& avTcij ro e^ tiplltovlov #cat ripnokiov 
30 8tao’r7j|/xaroy avveo-TTiKos (TV(TTr\pLa elkrj(l)6(o* eKTov be ro 15 
e^ fjpLLTovLov fcat roVoo. At piev ovv ra bvo [ra] irp&Ta 
k7](l)6evTa TTVKvd opi^ovcrai kuxavol etprjVTaL* rj be to TpiTov 
25 TTVKVOV opiQ^vera || ktxavbs eaTLV, fcoXetrat 

be TO xp&pia ev w eorlv TjpLLokLov. be ro TeTapTov ttvkvov 
5 opL^ovaa Xtxaz;oy eaTLV, KakeiTat | be ro 20 

Xp&pa ev & ecTL TovLalov. rj be ro TrepLTTTov krjipOev av- 
CTTipLa opL^ovaa kixdvos, 0 pLel^ov 'qbrj ttvkvov tjz;, eTreibriTrep 
Xcra eaTL ra bvo t& evC, ^apvTOTT] bidrovos eoriv. rj be ro 
io ^KTov kriipOev I (TV(TTr]pLa opC^ovaa Xtxawy o-wroz/tordirrj 

2 ex TO Me dvoTv H 4 5’ restituit Marquard 5 jutcvSvrav 
om. B 6 dvoTv H ivapfiovlcov . . . om. MVS: ivap- 

fiovloov Kal parvis litt. supra lin. reliquis omissis Me : ivapfiovicov re 
Kal reliquis omissis B R: verba in textu seripta restituit Marquard 
8 S restituit Marquard : d(fo Se M Va : Svo (Se et 

at omissis) S: Se Bvo rell. 9 clXrjfificvav (ai supraser.) B 

II ivapfiSvioi] iv supra lin. add., spin in a eras. Mb: ap/xSi/ioi BMa 
a’vvTov(&TaTai ex (rwrovd^raroi Ma (?) : <rvvTov<&TaToi V B : (rwrovoorar 
d* ai S 13 5* restituit Marquard 14 ^fiiroviov H 16 to 
del. Marquard 17 rh supra lin. B 19 rifii 6 \iov . . . iv ^ iari 
om. H : 7 ifjLi 6 \iov . . . om. R rh ante rjfjLi 6 \iov add. MVS 

22 5 ] % H fiii^ov Vb S : jxci^av M B R 24 o’va’Trjjxa^ (TTip.^'ta R 




bidrovos iortv. [m^v ovv ^apvraTr] y^pd^iariK^ ktyavos 
rrjs ivapfJLOVLOv ^apyrdvris €KT(o /x^pet rovov o^xrrepa icrrCv, 
i 7 r€LbriTr€p rj x/>a)|/xart#cr) bUcrts rrjs ivapfiovLov bUcrea)^ 8a)- 15 
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5 TptTTIpLOpLOV rov T^rdpTOV pL€pOV 9 bcobeKaTTJpLOpLCO V 7 r€p€X€LVy 
al b€ bvo yj)(»ipLaTiKoX r&v bvo [ ivappLovlcov brjXov &9 r£ 20 
blTTkaCTLCO, TOVTO 86 iorlv iKTTjpLOpLOVy ^XaTTOV bld(TT 7 ]pLa 
rov iXa^LCTov r&v pL€\(^bovpL€V(ov. Ta be roLavra d/xeXco- 
brjrd iariv, dpLeX^brjTov yap Xiyopiev o /xr) | rdirerai Kaff 25 
10 lavro ev ovarrjpiaTU be ^apvrdrr] btdrovos rrjs 0 apv- 
rdrrjy yj)()ipLaTiKr\s TjpLLTovLio Kal bcobeKarrjpLopLco rovov o^vrepa 
earLv. iifi /xa; yap rrjv rov rjpuoXlov Xiyavov | 

TjpiLrovLov dit avrrjSy dirb be rrjs tjplloXlov eirl rrjv evap- 30 
pLovLov bleaLSy dirb be rrjs evappiovCov errl rrjv fiapvrdrqv 
15 yj)(srpLariKr\v eKrTjpiopLoVy dm be rrjs fiapvrdrrjs \pc)rpiariKrjs 
errl rrjV fjpaoXiov boobeKaTqpLopLov rovov. ro || 86 reraprrj- 26 
pLopLov €#c rpL&v boobeKarripLopLoov ovyKeLrai, &(rr eXvai (pave- 
povy bn ro elprjpJvov 8 tdoTrj/xd eonv dm rrjs ^apxrrdrrjs 
biarovov errl rrjv | (^apxrrdrrjv xpcopLanKrjv. be avvrovo)- 5 
20 rdrrj btdrovos rrjs jBapvrdrrjs biarovov bueaei ian awrovoo- 
repa. ’E#c rovrcov 8 r) (pavepol yiyvovrab oi romi r&v Xiyav&v 
Ifcdorrjy i] re yap ^apv\repa rrjs xpcsrpianKrjs rrdcrd ecrnv lo 
evappLovLos Xlxclvos rj re rrjs biarovov ^apvrepa mad ecrri 

3 dadeKaTTffjLopiov MVS 4 fjLciCeav Vb: fieiCov M S Hoc loco 
in marg. M et Va et H multa adscripta sunt, quae videas in Comm, 
5 v supra lin. add. Mb 6 /col post add. 

MRVa 8 tSov iKax^fTTUiv H aix€\<6TrjTa S 10 cavrh 

ex cavTco Mb ry ante <rv<rT^/ioTi add. H ii, 12 in marg. Mx Vc 
haec : ^ afj ^ K XP^P-^ rh 5 /lera rov ^ 13 tj/xItopop H ott*] 

€7r’ R 14 ^Uffis ex BUffip Me : BUffip V B S ^16 dcKaryj^ 

fx6piop H in marg. MxVc haec: ipap/xop. dUcis (t6povT) rh 
Tcraprop 17 rpiap supra lin. Mb 3(i)d€KaT7jfiop(ov Ma, sed ap 

supra ov scr. Mb 18 rrjs om. Ma: ins. Mb 21 tottox ] 

t6poi B in marg. 22 fiapvripa Meibom : fiapurdrri codd. 

23 ipapfiSpios'] spin in a eras, ip supra lin. add. Mb ^ re] 

Kal fi H 



(x/>a)/xart#crj /x€xpt rrjs fiapyrarris xpoDfjLarLKrjs fj t€ rrjs bia- 
rovov (rvvTovayTdrqs ^apvripa Tracrd icm) bidrovos 
rrjs fiapvrdrrjs biarovov. Norjreoz; yap CLTr^Cpovs rbv dptOpov 
15 ray kLxavovs* ov yap | hv crri^crris rrjv (jxjDv^v rov aTro- 
b€b€Lyp€Vov kb^avci tottov Xi^avos €<rrat, bidK^vov 8’ ovb^v 5 
€OTt Tov kL)(avo€Lbovs TOTTOV ovb^ TOLovTov oXov pT] b^xeadaL 
20 kLXCLi^dv. "'ilo'T uvai pr] 7 r€pl puKpov r^v | dpipLafiriTricrLV 
oi p\v yap aXXoL biai^^povrai ir^pX rov biacrrripaTos povov, 
oXov TTorepov blrovos ioTLV tj Xlxclvos 17 (Tuvrovcorepa i)S ptas 
25 ovcrris ivappovLov fjpeXs 8’ ov povov ttX^Iovs iv | Ifcaorw 10 
y€V€L (papev eXvat Xlxclvovs piJds dXXa koI TTpoaridepev on 
dirnpol €l(n rov dptOpov. Ta p€V ovv Trepl r&v Xlxclv&v 
ovT(09 dcfxopLO-Oo)* TTapvTTarrjy be bvo elcrl tottol, 6 pev | 

30 KOLVOS TOV T€ bcaTOVOV Kal TOV XP^MOtroy, O 8’ €T€p 09 tbios 
rrjy dppovlas* KOLVcoveX yap Tq bvo yevrj t&v TrapviraT&v. 15 
evappovios pev ovv iaTl TrapvTraTTi Tracra rj fiapVTepa ttjs 
27 jSapvrcirrjy xP^Motrtfc^y, XP^P^'^^^V 8 taro||z;oy fj Xolttt] 

TTCLaa pixP^ dipcopiapevTis. T&v be 8ta<rrrj/xara)z; to pev 
VTTcirrjy #cat TrapvTrarrjy t& TrapvTTdTTjs Kal Xlxclvov tjtol icrov 
5 peXcobelTat rj eXaT\Tov, to be TTapvTTaTrjs Kal Xlxclvov t& 20 
Xlxclvov Kal pe(Tr]s Kal tcrov Kal dvicrov dpipoTepoos. tovtov 
8’ atTLov TO KOLvds eXvat ray irapvTrdTas t&v yev&v, yCyveTai 
10 yap eppeXes TeTp&xopbov eK 7rapi;|7rarrjy re xp^oMotrtfc^y (r^y) 
(SapvTdTTjs Kal biaTovov Xlxclvov r^y awToviOTaTTis. *0 86 

I €<rTi restituit Marquard 4 tos] to^s sed 

supra 0 ras. in qua a fuisse vid. Ma: rovs V S, B (sed ov in ras. et 
a suprascr.) oS ex ov Me : ov V S tov airodcdciyfi 4 vov tStto) 

Ma, sed od supra tov, (a supra airodedciyficvov et ov supra Xixavo) 
add. Me : tStto) Xixivo) V S : rSirov (« supraser.) \ixavov B 5 5’] 
y^p H 8 p. 6 vov H 9 ^irov 6 s Meibom: dtdrovSs eodd. 

avrris post /xids add. R 15 to add. Mx 16 eo’Ti] eri B : 

icrl B in marg. 18 rb jney . . . TrapvTrdTr}s om. R 20 t^] 

T^ S Ty KiXttPov om. R 21 afKporepas Marquard: dfi<poT€pois 

eodd. 23 rrjs fiapurdrifis eonieei : ‘jrapvTrdrTjs eodd. (R et B 

in marg.) : fiapvripas rivbs rrjs ripurovialas ante ‘irapwdrrjs add. 


APM0NIKi2N 2TOIXEI12N a I .27 

lijs TrapvTrdrTis tottos (pavepos icrvL €#c r&v epLirpocrdev, 
bcaLpeO^Cs re Kal crwreOels ocros icrrCv. | 

Uepl §€ crvvex^Cas Kal rod k^fjs dfcptjSaiy ov Trdvv 15 
pahiov iv dpxfj biopCcraL, TV7r(o be ireLpareov viTooTipLfjvaL. 

5 ^aCveraL be roLavTrj tls (pvcris elvai rov avvexpvs ev rrj /xeX- 
(obia ota Kal ev rfj ke\^eL irepl ttjv t&v ypapipidrcov (tvv- 20 
Oecriv* Kal yap ev r£ biaKeyecrOai (pvcreL fj (jxovr] Kad^ eKdcrrrjv 
T&v (rvXXal3&v Trp&rov ri Kal bevrepov r&v ypapipidrcov rCdTjcrL 
Kal TpLTov Kal rerapTov Kal Kara | rovs koLirovs dpiOpiovs 25 
10 axravro)?, ov ttclv pierd ttclv, dAA’ lort roiavrr] tls (pvaiK^ 
av^cris rrjs (rvvOecrea)^. 7rapa7rXr](r[oi)s be Kal ev rfi /xeA- 
(obelv ioiKev tj (jxovri riOevai Kara ovvexeLav | rd re biacrnfi- 30 
/xara Kal rovs (pOdyyovs (pvaLKrjv riva (rdvOecriv 8ta</)v\dr- 
Tovcray ov ttclv pierd ttclv bLdaTrjpLa piekcobovcra ovr^ tcrov ovr^ 

^5 dvLcrov. Zrjrrjreov be rb cruvexes ovx wy oi dp||/xoz;t#col ev 28 
raty r&v biaypapipidrov KaraTTVKViacrecrpv aTTobibovai Treip&v- 
raiy TovTovs aTTOTpaivovres riav (pOoyyov e^s dXXriXov 
KelcrOai 0I9 <n;/x|jS€jSrj#C€ ro lAd^toroz; bLdcrrrjpLa bUx^f^v dcp^ 5 
avT&v. ov ydp on [/x^] bvvarbv bUcreLS dfcro) Kal eiKocriv 
20 k^s piekcobrjcraL rfj (poovfj eariv, dXXd T 7 ]V rpirrjv biecrLv 
Trdvra TTOLovcra ovx 1 TrpoanOevaiy dAA’ cttI p^ev 10 

ro o^v eXdx^<^ov peXtobel ro Xolttov tov bid recrcrdpoVy —• 
rd 8’ ekdrTa) Trdvra e^abvvarel —^rovro 8’ ecrrlv rjroL d#cra- 
TTkdcnov rrjs eXaxCo'Trjs biecreos rj piKp& nvl | TravreX&s Kal 15 

2 (rvvTcdcls M V B S : awrid^Xs R : ipr^dcls Marquard 4 vvo<rrf 
fjL€ 7 pai S 7 ^ ® B KadcKaffTTj H 8 ri] re 

B R 9 XoiTTOvs om. H lo aW* ecrri . • . a’vpOda’cas om. M, 

in marg. Me (oi in roiavrrj in ras.): Vb in marg. sed roiavrri et ns om. 
Toiavrrj tis] ns a^rrj S ns om. B i6 ypafifiarap S 17 
ex ef ijs Me: ef V: i<l>€^rjs H aW^fiXap post K^laQai ponit H 

19 ov yhp jxSpop rh p}) d{fpa<rdai 5 . 0. /c. e. I. iJi€\cpd€ 7 a’dai rrjs (paprjs iarlp 
Marquard * 6 n eonieei: rod eodd. seelusi ^vparhp eonieei: 

dvpocrdai eodd. didais B 20 /xcKcp^rja’ai eonieei: ij.€Kep^€ 7 <rdai 

eodd. 24 SteVews] in ras. Mb 




a/xeXw8?/rw ^karroVy IttI h\ to ^apv r&v dvo bUo-ecov roviaiov 
ikarrov ov bvvaraL [xekiDbelv. Ov 877 TrpocreKTeov €t to 
20 crwe^es ore pL€V lacov ore 8’ e£ avCcrcov ytyz;erat, | akka 
TTpos T^v Trjs pL€k(ob[as (pyo-Lv 7 r€LpaT€ov jSXeTretz; KaTavo^lv 
re 7rpo6vpiovpL€Vov rt /xera rt irecpvKev rj (jxov^ bido-TripLa^ 
TiQivai Kara /xeXos. et yap /xera TrapvTrdTrjv Kai kb^avov /xtj | 

25 8oz;aroz; eyyvrepo) pLekiobrjaai (pdoyyov /xeo-r/s, avr?/ &z; efrj 
/xera rrjz; kvyavovy etre bmk&crLov etre irokkaTTkAcrbov 8ta- 
o-rrj/xa opt^^L (roS) TrapvTrarr/y Kal kL\avov. Tiva /xez; ovz; 

30 TpoTTov TO re o-wex^s Kal | ro e^rjs 8et C^retz;, (jx€8oz; brjkov 10 
€K T&v €ipripL€V(»)V 7 r &9 8e yiyv^Tai Kal rt /xera rt 8tclio’rr7/xa 
29 TbO^Tai re Kal ov rt^erat, ev roty 11 o-rotx^toty b^LyOrjcrerai. 

^T 7 roK€L(r 6 (ji) /xera ro ttvkvov rj ro airuKvov rt^e/xevov 
(TV(TTr\pLa eTrl /xev ro o^v /x^ TiO^crOaL eXarrov biaaTqpia tov 
5 k€LTTopL€Vov Trjs | TTpcSri/j aypLcpcovCaSy eTrl 8e ro jSapv /x^i 5 
eXarrov Tovialov* VTTOKeto’^o) 8e Kal rfiv e^^y K€LpL€V(>)V 
(pOoyycov KaTa /xeXoy kv eKao-rw yevet ^rot roi/y reraprovy 
10 [roty rerpao-t] 8ta T^TTapcov o-v/xlc^covetz; ^ rovy 7re/x7rrovy 
[rots TTevre] 8ta Trevre ^ d/x<^orepa)s* w 8’ dv r©z; (pdoyycov 
pLTjbev fj TovTiov oT/xjSejSr/Kos, eK/xe\^ roiJrov etvat Trpos rovs ots 20 
15 aovpLcpoovos io’TLv. *T 7 roKe^o‘ 0 a) 8e Kal | T^TTapcov yiyvo- 
pL€V(ov biacTTTipL&TOiv €V tQ 8td TTevre, dvo /xev ^o-coz; ws eTrl 
ro TTokVy T<oy to ttvkvov ' KaT^xovTcov, dvo 8’ aviacovy rov re 

k€LTTOpL€VOV TTJS TTpcSri/S <TVpL(p()ivlaS Kal Ttjs VTrepOX^J? 2? TO 

20 8td I 7 r€VT€ TOV 8td T€(r(rdp(i)v vTrepex^t, kvavTws Ti6€(T6ai2^ 

I ^ in ras. Mb tKarrov Meibom : ihirrovi M V S R : 

eKarrapi B roviaiov Meibom : roviaiav M V R : roviouov B S 

2 cKarrov supra lin. Mx. om. Va, add. in marg. Vb H 

5 ))] 56 H €1 conieci: cis codd. 7 dvvarhv om. B : dvvar^ S, Vb 
(sed ^ in ras.) 9 rov restituit Marquard 12 t€ om. H 

13 ix€T^ conieci: fihv codd. rh &irvKvov ex rhv irvKvhv (ut vid.) Mb 

14 TldecdaC^ ficrarldco’dai M 15 Koiirofievov H 18 to7s 

rirpaai del. Meibom 19 ro7s TreVre del. Meibom 20 ^vai 

om. H To\)s ofs] rovrois R 24 Koivofievou H ^ ex ^ Mb : 

^ S rh ex TOV Ma (?) S : rh Vb cum ras. post h 25 vircpcx^i 

Meibom: vircpcx^iv codd. 




7rpo9 TOLS IcroLS ra [be] avicra €7rt re to o^v #cat to fiapv. 
^TiroKeLcrOoi) be Kal tov9 tol 9 e^rjs <^0oyyoty (rvpLcjxovovvTas 
8ta Trjs avrrjs 0DpL\^(»)vCa9 e^rjs avToXs eivau ^AoijvOeTov be 25 
VTTOKeCcrOa) ev eKaorco yevei elvai bL6.(TTr\pLa KaTa pLe\o9 b fj 
5 (fxovrj pLekiobovaa pj} bvvaTai biaipelv eh biaarripaTa. ‘Ttto- 
KeicrOoa be Kal tS^v avp(l)<o\voi)v eKacrTov biaipeicrOaL els 30 
acrvvdeTa irdvra peyeOrj. ’Aycoyrj 8’ Icrra) ^ 8ta t&v e^fjs 
(^Ooyyoiv {&v), eacoOev t&v aKp(ov, [&v] ev {eKdcrTov) eKa~ 
Tepoodev daijvOeTov KeiTat bidoTripa* evdeXa 8’ ^ eirl to avro. 

I de del. Meibom re om. R rb ante Pap^u om. S 2 robs 

ex rb Me : rb V S <rvfi<po)vovvTas ex <TVfjL<p^vov r&s Me : <TVfjL<p(avov 

rks V S : Ka\ rb (rvfjL<p(ovov riis in marg. B 3 abroTs Marquard : 

avroTs eodd. 4 ante h una litt. eras. M tj supra lin. add. Mx : 
om. VS ^ ante rj add. B 5 <pa>v^^ ^ in ras. Vb bida’TTjfxa 

B sed in marg. biaariifiara 7 irdvra supra lin. add. Me : om. V S 
8 S>v addidi ccadcv eonieei: eodd. IkKpccv eonieei: apx^v 

eodd. &v seelusi : supra lin. B Vb ; 

antea in utroque eod. laeuna erat: IS: h rell. kKa<rrov addidi 



30, 10 BeArtoz; Xcrcos icrrl to 7 rpobL\€\d€LV rov rpoTrov rrjs Trpa- 
ypLareias tls ttot €ot(v, tva 7rpoyLyv<o(rKovT€S &(r7r€p obov if 
^abicrriov pqbiov TropevdpieOa elbores T€ Kara ri pL€pos kcrpi^v 5 
15 avrrjs | Kal /xrj \dd(opL€v fipJas avrovs 7 rapv 7 rokapifidvovT €9 to 
TT pdypLa. Kaddirep ’AptororeXijy del Strjyetro rovy TTkeLCTovs 
T&v aKovcrdvrcov Trapd n\dra)z;oy Trjv Trepl Tayadov aKpoacriv 
20 TradeLV. | TTpoaUvaL pL€V yap efcaoroz; vTToXapi^dvovTa Xtj- 
xl/^aOaL TL T&v vopLL^opL€VOi)v TovTcov dvOpooTTLVOov dyaO&v dtov 10 
TiXovTov vyUiav icryyv to oXov €vbaLpLOv(av TLvd OavpLacrTriv* 

25 ore be | ipaveCrjaav ol XoyoL irepl /xa^rj/xdrcoz; Kal aptdpi&v 
Kal y€(»)pL€Tp[as Kal dcrTpoXoyias Kal to Trepan otl dyaOov 
31 icTiv ev, TravTeX&s olpLat TrapdboW^dv tl i(f)aLV€To avroLS" 
eX0* oi piev v'noKaTe(^p6vovv tov TrpdypiaTos ol be fcare- 15 
fJLefJL(f)ovTo. Tl ovv to aiTiov; ov Trporjbecravy dXX^ &(r7rep 
5 ol epLCTTLKol I Trpoy Tovvopia avTo v 7 roKe\riv 6 Tes irpocrpecrav 
el be ye tl 9 otpLai Trpoe^eTLdeL to oXov, aTreyLVcoaKev av 6 
pLeXXcov aKoveiv 17 el'nep rjpecrKev avT^ btepLevev dv ev rj) 

10 elprjpLevr] vTToXiplreL. | ITpoeXeye p.ev ovv #cal avTos ^AptcrTo- 20 

3 Trpo€\d€ 7 i/ {di suprascrO B 4 ris Marquard: rl codd. 

6 TrapvTroKafjLfiav 6 vT(av Ma, sed es supra ct>v scr. Mb 11 ttKovtov^ 

post 0 ante v ras. M vyciay M V B S ev^aifiovias rifi^v R 
12 de supra lin. add. Mb 17 oi om. lac. 4 syllabb. R 18 irpo- 
€^€Tid 7 ) Ma praeter drj quod cum ei superposito ab Mb in ras. qua plus 
una littera deleta erat ivcyii/axrKci/ ex airey, M : iir^yIvuiffK^v 

rell. 19 Koii infra lin. ante ^ add. Mb 20 ciArifjLficvtf 




II. 31 

rekrj^ bi avras ravras ray alrCas, <5)9 tols fieWovcrtv 
CLKpoacrdaL Trap’ avrov, 7r€pl t(v(ov t icrrlv tj irpaypLar^La Kal 
TLS. B^Xtlov §€ Kal TjpXv I (f>aLV€TaL, KadaTT^p €t 7 ro/x€z; €z; 15 
apxfjf TO Tipo^ibivau Ttyv^rai yap €Vlot€ €<^’ kKarepa 
5 apLaprCa* ol piev yap /x€ya tl vitoXapL^avovaiv elvai to 
piddripLa Kal ^aeo-Oai evLOL piev ov pLo^vov pLovauKol clkov- 20 
(ravT€S ra appLovLKa, dWa Kal j^ekrtovs to Tj^oy,— TrapaKov- 
aavT^s T&v iv Tats b^L^ecrt k6y(ov otl 7r€Lp<opL€da Troieiv t&v 
pL^koTTOU&V kKaOTrjV Kal TO bkoVy TTjS pLOVCLKrjs I OTL 7J 25 
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dxfyekeLV ovb' aKovcravTes oXcoy —ol be TrdkLV wy ovbev | aAA’ 30 
rj pLLKpov TL Kal fiovkopievoL /xrj etvaL epLTreLpoL pLrjbe tl 'hot 
ecTTLV. OvbeTepov be tovtcov dkrjOes eaTLV, oijTe yap evKaTa- 
15 cfypovTjTov ecTL TLVL 09 vovv exeL TO pidOrjpLa — brjkov 8 ’ eoraL 
Trpotoz;| |roy tov koyov—, ovTe TrjkLKovrov &ot avTapKes 3 ^ 
etvaL Trpoy irdvTa, KaOd'nep otovTai TLves. Trokka yap 8rj #cat 
eTepa v'ndpx^^ [^] Kaddirep del keyeTaL r£ | plovo-lkQ* piepos 5 
ydp ioTLv 17 dppLovLK^ TTpaypLaTeia Trjs tov piovaLKov e^eoos, 

20 KaOdirep rj Te pvOpLLKT] Kal rj /xerptfcrj #cat rj opyavLKTj, AeKTeov 
ovv TTepl avrrjs Te Kal tQv pLep&v.\ 

Kadokov piev ovv vorjTeov ovcrav ripLLv ttjv Oeoopiav ire pi 10 
pLekov9 rravTos Troiy iroTe 7re(l)VKev fj (fxovri eTTLTeLVopLevri Kal 
dvLepLevrj TLOevaL ra 8 taoT 7 j/xara. <^i;|(rt#cr)z; ydp brj TLvd 15 

I €<l>7j conieci: €<l)r)v codd. 3 Kal rjfjLii/~\ Kal om. R 6 fxhv 

in ras. M : 56 pro fihv B R ia^aQai post fjikv ponit Marquard 

aKovovr^s {(rav suprascr.) B 7 Kal om. B vapaKovov 

res B 9 fi^XoiTTOiav S kKdffrrjv Kal om. R ii Kal ante 

Kad* * 6 <rov add. Marquard 12 ^ Marquard: aWa codd. 

13 ^fjLircipoi conieci: ^Treipoi codd. firj^k tl ttot iariv] firfidri 

TrapiffTLv R 14 ayvociv Trp6<r€ia’i post ttot* iarlv add. Marquard Se] 
ykp R a\7)d€S ecrrii'] iariv om. R lac. 15 iari tlvl %5 vovv ex^t 
conieci: iariv as vvv ^x^t codd. 16 \6yov om. R lac. afjrapK^s 
om. R lac. 18 ^ seclusi tovto post ^ add. Westphal ael 

om. R 20 KOLi 7! fX€TpiK^ om. R 22 oi/(r7js tj/jliv Trjs dcaplas H 
24 5 ^ om. B 




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20 6 fJLO\oyOVIJL€Va 9 Tois <paLVOfJL€VOLSy OV Ka\ 6 d 7 r€p ol €pL 7 rpO(r 0 €V, 
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25 (^d(TK 0 VT€S Koyovs T€ TLvas dpiOpL&v elvat | Kal rd^rj Trpoy 
dWTjka iv ots to re o^v Kal to ^apv yCyveTat, 7 rdvT(ov 
(paLVopL^voLS* ol 8’ d'HoO^cr'Ki^ovT^s €Ka(rTa av€v alTias Kal | 

30 d 7 rob€L^€ 0 i)S ovb^ avTa ra (paivopi^va Kak&s €^pt 0 /xrj#cor€y. 10 
^H/x€iy 8’ dp\ds T€ 7r€tpa)/x€0a XafSeLV (patvopievas h'ndcras 
33 ToXs ipL 7 r€LpoLS pLovcTLKrjs Kal Ttt €K TovTiov (rvpL\\^aLvovTa 

*^EoTt 8^ TO pL€V okov r]p!iv (17) Oecopta Trept piekovs TravTos 
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5 8’ 71 irpaypLaT^Ca | els bvo, eis T€ t^v aKo^v Kal els rrjz; 8ta“ 
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pLeyiOrj, Trj be biavoia deaypovpLev tcls t&v {(p66yy(ov) bvvdpLets* 

10 Ael ovv eTredLadrjvaL eKacTTa | aKpi^&s Kpiveiv. ov yap eaTiv 
&(r 7 rep eirl t&v btaypapipidTcov etOLO-Tat keyecrOai* €<rra) roSro 20 
evOela ypapLpLrj, —ovtoo Kal €m t&v 8taoTrj/xara)z; elirovTa 
15 aTrqkkdyOaL [8€t]. piev yap yeoopLeTprjs | ov8€z; xprjTat Trj 
Trjs alaOrjcreLos bvvdpLet, ov yap eOi^eL t^v o\pLV ovTe to evdv 
ovTe TO 7 repL(pepes ovt^ akko ovbev t&v tolovtcov ovTe (pavkoos 
20 ovTe ev KpiveiVy dXSh pidkkov 6 TeKTcov Kal | o TopvevTrfS Kal 25 
eTepai Tives t&v Teyy&v irepl raSra TrpaypiaTevovTar r^ be 
pLova‘LK& (r\eb 6 v eortv dpxrjs eypvcra Td^iv rj Trjs alaOrjaeiOS 

I ovx OVK et as supra lin. M 2 \e\4yeip S 5 oStrap 

post aKpifiri ponit H ovk om. S Kal post 5 ^ add. R t rh 

Papv H : rh om. rell. 8 ipapriordrovs B 9 avorcpvl^oprcs H 
II aTracas om. R lac.: S,Tra<n H 14 ^ restituit Marquard 16 re 
om. B 18 Toop <pd6yyo)p conieci: rovrap codd. 19 iTrcdKrdripai^ 
ivcdi in ras. Mb : idia’drjpai R, in marg. B 21 o^tw] post a litt. 

<r eras. M 22 awriKKax^^pai H $6? seclusi rjj add. Mb(?) 
23 oi;T€ ^vQv om. R 27 ^ supra lin, add, Ma (vel Mb) 



n 33 

afcptjSeta, ov yap kvh^y^Tai (l)avXoi)s al(rdav 6 pL€\vop eS Kiy^iv 25 
TTcpt TovTdiV &v pLr]h^va TpoTTOv aicrOav^Tai. ^Eorat h\ roCro 
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fj rfjs [MovaLKrjs ^v^cris a/xa piivovTos nvo 9 | Kal Kivovpiivov 30 
5 kern Kal rbvro (ryebov 8ta TraoTjy Kal Kara ttclv fikpos avTrjs, 
i)S elirelp clttXQs, bianiveiv. Evflecoy yap ray r&v yev&v 
bLa(l)opas alaOavopieOa rod p.\v 'nepUyovros pikvovTos, r&v be 
[leo-iov KLVovpieviov Kal Trakiv 11 orav piivovTos rod pieyeOovs 34 
ro8€ piev KaX&piev virarriv Kal piearjv, robe be 'napapLeerqv #cat 
10 vrjrriv, pievovros [ybp] rov pieyeOovs (rupL^aCveL KiveLcrOat ray 
T&v I (l) 66 yy(ov bwapLets* Kal Trdktv orav rov avrov pieyeOovs 5 
TTkeLO) oyripLara yLyvTjraLy KaOdirep rov re 8ta reo-adpeov Kal 
bta irevre Kal erepcov waavreoy be Kal orav rov avrov 
8ta(rrrj/xaroy ttoS | piev ndepievov pLerafioXrj yiyvr]Taiy ttov be 10 
15 piTj. YldXiv ev roty rrepl rovs pvOpLovs ttoWcl rouavO^ op&piev 
ytyvopieva* Kal yap pievovros rov \ 6 yov #ca0’ ov bidpLoraL ra 
yevTj ra pieyeOr] KLveL\TaL r&v irob&v 8ta rrjv rrjs ayayyrjs 15 
bvvapnvy Kal r&v pieyeO&v pLevovreov avopLotot yiyvovrai oi 
TTobes* Kal ro avrb pLeye 6 o 9 Troba re bvvarai koX (Tv^vyiav* 

20 brjkov 8* on Kal (at 8ta<;^opat) at r&v bLaLpeo‘e\dv re koI 20 
(ryrjpLdroov Trepl pievov n pieyeOos yiyvovrai. KaOoXov 8’ 
elireiv rj piev pvOpiOTroua TroWay #cat TravrobaTras KivYjaeis 
Kiveiraiy ol be Trobes ols aripiaivopLeOa rovs pvOptovs aTrXay 
re I fcat ray avrds del. 'Toiavrr]v 8’ eyovoris (^vatz; r^y 25 
25 piovaiKfjs dvayKOLiov fcat ev roty Trepl ro rippLoapLevov awe- 

I ov Marquard : oi/re codd. al(rdav 6 fi€vos B 2 rav B : &v 

in marg. 3 €7r'] air* H 4 fiivovros ex fiiv ivros Me : ficv 

ivTos Va B 5 avTrjs om. H 10 yhp seclusi avfjLfialv^i 

. . . ficykdovs om. S 12 yiverai Ma (sed tf suprascr. Me) 

VBS 13 5 iek TreVre] 5 iek supra lin. add. Me: om. VS, B 

(sed add. in marg.) 14 ttov fi€P] iroiovfi^v H ylvcrai 

SR 16 Ka 6 ^ hv ex Kadh Me: Kadh VSB 19 to 

airrh eonieei: ainh rh eodd. 20 at diaipopal addidi (Jdiaipopal 

post o'xnV’kLTOiv addidit Marquard) at ray] at om. R H 21 Trept- 

IxkvovTi B 




OtaOrjvaL tt^v re btdvoLav Kal rrjv atcrOrjcriv Ka\&9 Kpiv^iv to 
30 re fJL€vov Kal to kl\vovijl€Vov. ^AttX&s fiev ovv etTretz; TOLavTrj 
tCs eaTLV fj apfiovLKrj fc\rj0et<ra emcrrTj/xr) otav bLeXrjXvOapLev* 

(TV/xjSejSrjfce 8’ avT^v Statpeto-flat ety eTrra /xeprj. || 

35 icTTlv kv pL€V Kal TTp&Tov TO biopicrai Ta yivr] koX 5 

'noiTfcrai (I)av€p 6 v, tlvoov Trore pL^vovTcov Kal tlvcov KLVovpL€VOi)v 
5 al bLa(l)opal avTau yiyvovTau Toi 5 |ro yap ovbels 7 r( 07 rore 
8 t(opt(re TpoTTov TLva etfcorcoy ov yap iirpaypiaT^ijovTO Trepc 
T&v bvo y€v&Vy aXXa Trept avTrjs Trjs appiovias* ov pLTjv aX)C 
10 oX ye 8 tarp(jSoz;rey Trept ra opyava bijicrOdvovTO | piev kKdcrTov 10 
T&v y€V&Vy avTo 8 e ro Trore ap\€TaL e^ appLovCas yfi&pid ti 
yiyv^crOaL, ovbels ovb^ eTrejSXe'v/^e 'irdiroT avT&v. ovt€ yap 
Kara irdcrav yjpoav kKdcTTOv tQv y^v&v biricrOdvovTo bih ro 
15 /XT^re I TrdoTjy /xeXoTTottay e/x 7 retpot e?z;at /xrjre crw^iOiaQai 
Trepi rdy ToiavTas btaipopds aKpi^oXoy^icrQai* ovt avTo 15 
TTO)? roSro KaTepiaOov otl tottol tlv €9 ^crav t&v KLvovpL€VOi)v 
20 (pOoyycov iv raty | rSz; yev&v bLatpopaXs. At’ /xez; ovv 
ahias ovk tjz ; bio^picrpLiva rd yivr] Trpdrepoz;, 07(e8dz; eto-tz; al 
€lpripL€var otl 8e Stoptoreoz; et /xeAXo/xez; aKoAovfletz; raty 
25 yiyvopL^vais kv roty /xeAeo-t 8ta|</)opaty, (pavepov. 20 

ripSroz; /xez; oSz; rSz; pL€p&v eo’rt ro elpTjpikvov 8evrepoz; 

8e ro Trept btacTr]pidTcov etTretz;, pLTjbepLLav t&v VTrap- 
30 ypvcr&v avTOLS btacpop&v ety bvvapnv 7rapaAt/x|7rdz;oz;ray. 

z; 8e, wy olttX&s etTretz;, at TrAetovy avT&v eicrlv a 0 e(o- 
prjrot. ov 8et 8’ dyvoeXv, otl Ka0’ ^z; dz; yez;c 5 /xe 0 a rSz; 25 

I 61 ante /caAws et PovXoifxeda ante Kpheiv add. H 3 K \€ id € 7a’a B 
5 Biopiaai ex diaplffai Ma 6 Trore om. R /cal Marquard : ^ 

codd. 8 dio ) pi<rai (e suprascr.) S 10 ye] /lei' H ii Se 

in ras. Mb, fuisse vid. /iei^: ficvroi R 12 oijTc Marquard : ovSe 

codd. 15 ov 5 * R 16 Karcfiadov Marquard : Karcfi'fivvop H : 

Korafiivovd ^ rell. ; KarafiadSvrcs Meibom ^re H 17 to?s (o 

suprascr.) B 20 /ieKeai conieci : ycpcci codd. : post to 7 s 

dat jueA S sed deletum 21 fihp om. H 22 virapxovo’ap 

ex vmpx^PTap Ma 23 TrapaKifnravovrai (ut vid.) B: TropaXt/i- 

irdvovT^s H 




€KkLfjL 7 ravov(r&v T€ Kol aO^ooprjroiiv hia(^op&Vy Kara TairTjv 
ayvorj(TopL€v || ray iv roty pL€X(^bovpL€VOLS buaipopds. 36 

’Ettci 8’ icrrlv ovk avrdpKTj rd bLaan^pLara Trpoy t^v t&v 
(l) 66 yy(ji)V bidyvoixnv—irdv ydp^ coy b/nX&s etTreti;, StajoT?/- 5 
5 /xaroy /x€y€0oy TTk^Lovcov tlv&v bvvdpL€(»)v kolvov icrriv —, 
rpLrov dv ri /xepoy €trj rrjs oKrjs Trpay/xaretay ro 7 r€pl r&'v 
<l) 66 yyoi)V octol t elcrl koI tlvl yvaypiCovraL koI tto- 

T€\pov rdcr^LS rivis elcrtv, &(T 7 r€p oi ttoWoI v'noXapL^dvovcriVy 10 
^ bvvdpL€L 9 Kal avTo TOVTO t( ttot iorlv fj bvvapus. Ovb^v 
10 yap T&v TOLovTcov bioparai KaOap&s vtto t&v ra TotavTa 
irpaypLaTevopiAvcov. \ 

T^TapTov 8’ &v €trj /xepoy ra crvcrTijpLaTa OeaypfjcraL 15 
TTocra r’ icrTl Kal ttol arra Kal tt&s €K T€ t&v bLaoTTjfjidToov 
Kal (l)ddyy(t>v crvveoTTjKOTa. OvbeTepov yap t&v TpoTrcov 
15 r€0€(o/5rjrat ro pApos rovro vtto \ t&v ipirpocrd^v* ovre yap €t 20 
TkdvTa TpoTTOv €#c T&V biacrTqpdTOdV (rovTiQ^Tai ra avor/jpaTa 
Kal prib^pia t&v avvOicr^oiv Trapd (I)vo‘lv IcttIv €7rt(rK€\/r€a)y 
T€TV)(r)K€Vy ov 6 ^ al bLa(l)opal TrdcraL t&v (rvo‘Tripd\T(»)v vtt ov- 25 
8^z;oy i^ripCOpriVTaL. Uepl p\v yap ippeXovs rj eKpeXovs 
20 aTrX&s ovbeva Xoyov TreTroLTjVTaL oi Trpo fjp&v, t&v be (Tuott]- 
pdT(ov ray btaipopds ol pev oXcoy ovk eTiexeipovv i^apiOpeLV | 

—dXXd Trepl avT&v povov t&v iTrra oKTaxopbiov h eKdXovv 30 
dppovCas TTjv eTTLCTKeyl/Lv eTTOLovvTo —, oi 8 ’ eTnx^ipricravTes 
ovbeva TpoTTov e^rjptOpovvTOy KaOdirep oi Trepl UvOayopav 
25 roz; ZaKvvObov Kal ’Ayrj||z;opa tov MtTvXrjvaLOv. "^Eort 37 

I €K\ifjLTrav 6 vTQiv Ma (sed ovffSov suprascr. Me) VBS: iKKifiiravo^ 
fjL€ua>v H 2 ayvoiiafafi^v M (ut vid.) V B 6 dv ri post fiipos 

ponit H 7 TLvi ex Tiva>v coir. S 10 Kadapas om. H 

12 d€a>p€i(rdai H 14 rav ante (pdiyycov et ffva’TruiaTa ante ovvcffTTi^ 
Kora add. H ovderepov^ ov et 4 in ras. Mb 16 o’va’T'fifiara^ 

in ras. Mb, fuerat fortasse 5 io<rT^ 19 fxcv om. H ^ H 

21 ctTrcx^lpovv H 22 ix 6 voiv H kirrh oKrax^pdav Westphal: 

iwTax^pdav codd., sed in M a poster, manu ex inrd xopSwi' factum 
23 T^v om. H 24 T€ ante ir^pX TivQaydpav et oi vepi ante *Ay4ivopa 
add. H 




be TOLavTrj tls fj Trepl to e/x/xeXey re Kal eKfieXes rd^LS 
Ota fcat Tj Trepl {rrjv) r&v ypapipidrcov crdvOecriv iv rS 
5 btakeyecrOar ov yap 7 rdv\Ta rpoTTov €#c r&v avr&v ypapL- 
pLarcov (TVVTiQepLevr] ^vWal 3 ^ yCyverat, dXXa Trtoy piivy tto)? 

8> V 

ov. 5 

YlipLTTTov 8’ ecrrX r&v piep&v to Trepl tov 9 tovovs i(f>^ 
lo &v TiOepieva ra (rv|(rr7j/xara /xeXwSetrat. Ylepl &v ovbels 
ovbev eLpTjKeVy ovTe Ttva Tpoirov XrjTrreov ovTe Trpbs tl jSXe- 
TTovTas Tov dptOpLov avT&v diroboTeov ecTTiv. dXKa 'navTeXSiS 
15 €ot#C€ T&v ripL€p&v dy(oy^ t&v \ dppLOVLKcav 17 Trepl t&v tovcov 10 
d'nobocriSy oXov oTav Koptz; 0 tot p^v beKdTTjv ayaxTLv ’A 0 rjz;atot 
be TrepTrTTjv eTepoL be Tives dyboTjv. ovto) yap ol pev t&v 
20 appovLK&v Xeyovcri ^apVTaTov pev tov | v 7 rob<opLov t&v 

8 ’ TJpLTOVLip TOV b&piOVy TOV be boOpLOV TOVip TOV (f)pvyLOVy 15 

25 &(ravT(i)s be Kal tov (f)pvyLOv tov XvbLov eTep(p Tovip* ere|pot 
8 e Trpoy rot? elprjpevoLs tov VTTOippvyLov avXbv irpoorLdeacLv 
em ro jSapv, ot 8 e av Ttpos TTjv t&v avX&v TpvTrqcnv jSXe- 
T^ovTes rpety pev tov 9 ^apvTaTovs TpLcri bUcrecriv d/n 
30 dXXT^\X(i)v yaipi^ovaiVy tov re viroippvyLov Kal tov VTrob&pLov 20 
Kat TOV b&pLoVy TOV be (l>pvyLov dm roi; boopCov Tovipy tov 
be Xvbiov dm tov (l)pvyCov TrdXLv Tpets bieaeLS dipLorrdcrLv 
&(ravT(i)s 8 ^ #cat tov pL^oXvbtov tov Xvbiov. Tt 8 ’ eo’rt irpos 
38 o fiXemvTes || ovtco mieXcrOai tt]v bidcTTaaiv t&v tovo^v 
T rpoTeOvprivTaLy ovbev eipriKacriv. *^Ort be ecrTiv tj #cara- 25 

I T6 om. H rh ante iKfieKes add. H fi supra lin. add. Ma : 
om. H 2 restituit Marquard <rvpB€<riv Meibom : 

codd. 6 r6povs] prior, litt. in ras. Vb (Va fort. rpSnovs) 9 ia-rlp 
om. H 10 tt) • . . o'yw'yrj linea subducta S rj/i€pap~\ ri in ras. 

Mb, erat rap fiepap Trepi] rap B : om. S ii Koplpdioi • . . 

oyBSrjp linea subducta S 13 elpai post flip add., rhp ^vodcopiop 

om., rh viroBdiipiop post rSpap add. H 14 prius rot/rov] to6tov Me R : 
To^Toop Ma rell. alterum TotJrov] tovtov Me : rolfToop rell. 17 ^rphs 
om. H 18 rpi'irrta’ip H 19 dl post rpitrl add. VSB 21 Kal 
rhp da&piop om. R 25 Trporcdvfirjprai ovdlp ^ip'ljKaa’ip supra lin. 

add. Mb 



TntJKvaycrLS €#c/x€\^y koX irdvra rpoTTov axpTjcrroSy (f)a\V€pov iir^ 5 
avrrjs lorai rrjs TipaypLar^ias. 

’EtTcI §€ T&v pL€\(aboVpL€V(»)V icTTL TO, pi€V CLTlXcL Ttt §€ /X€- 
rd^oXay 7r€pl pL^ral^oXrjs av a,r\ keKriov, Trp&rov | pi€v avro 10 
5 rt TTOT icrrlv fj /x€ra/3oA^ koX tt&s yiyvops^vov —^Aeyo) 8’ oXov 
TrdOovs rivos crvpL^aivovros iv Tjj rrjs pLeXcobias ra^€t—, 
€7r€tra iiocrai elcrlv al 'ndcrai pL^ral^oXal koX Kara Trocra | 
8taoT7j)utara. He pi yap tovtcov ovbels ovbevbs etprjrat Aoyoy 15 

OVT^ d7Tob€LKTLK09 OVT dvaTTob^LKTOS* 

10 TeX^vratov be r&v (jxep&v ecm) to Trepl avrrjs rrjs pie- 
XoTTOitas. ^Errel yap iv tols amols <^0oy|yoty abiaipopoLS 20 
oven TO Ka 6 * avrovs rroXXai re Kal iravTobaTral piopcpal pieX 5 >v 
yiyvovTaLy brjXov on irapa ttjv yjp^env tovto yevoir av. 
KaXovpiev be rovro pieXoTrodav. piev ovv rrepl to rippio- 
15 erpievov | TTpaypLareia bta tQv elpripievcov piep&v iropevdeXcra 25 
TOLovTov Xi]\lreTaL reXos. 

"'On 8’ e{o‘TT) to ^vvievai t&v pieXi^bovpievcov Trj re aKorj 
Kal rrj biavoia Kara Tracav bta^opav tols ytyvopie^voLS rrapa- 30 
KoXovOelv {brjXov)—ev yevecrei yap 8r) ro pieXoSy KaOdrrep 

20 Kal ra Xotira piept] rrjs pLOVcrLKrjs —. 

. eK bvo yap rovnsrv rj rrjs piovcrLKrjs ^vecris eernvy 

al(r6i](re(is re Kal pLvrjpirjs" al(rddve\\(r6aL piev yap* bet to 39 
yiyvopievovy purqpioveveLV be to yeyovos* Kar aXXov be rporrov 
ovK ean tols ev Tjj pLovcrLKrj irapaKoXovOeLV. 

3 fierdfioKa Meibom : d/icrafioKa codd. 5 K^yoi] Ae S 6 rivos 
conieci: rivhs codd. 7 iraffai post /icraPoKal ponunt R H 

8 ovdels post ovdcvhs ponit H 9 awSdciKTos B 10 ficpav 

icTi restituit Meibom : rav /icpav iffri om. R: /icpav icri rh om. 
rell. ficKoiroitas Meibom H : /xcKcpdias rell. 12 rb om. H 

fiop<pal om. B, sed a corn supra lin. add. /jL€\av post yiyvovrai 
ponit H 13 7ra/)^j irphs H 14 pLcKairodav S odv~\ av B 

16 ToiovTov ex ToiovTo Me: roiovro VBS 17 iari addidi 

%Ka<Trov post fi^KtpbovfiivoiV add. Meibom 18 TrapaKoKovdcTv 

conieci: TrapaKoKovdcT codd. (post e? ras. M) 19 drj\ov addidi 

rh supra lin. add. Mb 21 e/c 5 t;o . . . fjLOvaiKris in marg. Mb 

22 aia’ddv€<rdai ftey] ai fiiv e coir. B dei ex 5^ Me; 5 ^ V B S 






5 §€ TLV€9 TTOLovvraL T€\r] rrjs | apfiovLKrjs Kakov- 

fjLevTjs 7rpayfjLaT€Las ol piev to TrapaarjpLaCvecrOaL ra /xeArj 
(pdcTKovres 7r€pas ^Xvai rov ^vvUvai r^v pL€K(obovpL€V(ov 
^KaCTTOVy ol §€ TTIV TT^pl TOVS avkoVS O^OOpCaV Kal TO 
lo €;(€tz; I €l7r€LV TLva Tpoirov ^KacrTa tQv avkovpL€Vu)v Kal 5 
TToOev yCyv^Tai* to 8 r) TavTa kiy^iv navT^k&s kcTTiv bkov 
TLVOS bLTJpLapTTJKOTOS. Ov ydp OTL TlipaS Tr]9 appLOVLKrjs 
15 €7rt<rr7j)utrjy korlv rj 7rapa(rrj|)utaz;rt#c7j, dAA’ ovbe piipos ov- 
b^Vy €t pLr\ Kal Trjs pL^TpLKrjs to ypdxl/aaOaL t&v pL€Tp(ov 
^KacTTov* €t 8 ’ &(r7r€p iirl tovtcov ovk dvayKalov icrTL 10 
Tov bvvdpL€VOV ypdxl/aaOaL to lapi^iKov (jx€Tpov Kal elbevaL 
20 TL icTL TO lapL^LKOv), | 0VT(09 Ix^t Kal €776 T&V pL^kipboV- 
pL€V(»)Vy—OV yap dvayKoXov kcrTi tov ypaxj/dpLevov to (l)pvyLov 
pL€kos Kal ^ibivai tl icrTL to (l)pvyLov piikos—brjkov otl 
25 OVK &v €?rj Tr]9 elprjpLivrjs | iincTTrjpLris rripas rj Trapacrr]- 15 
pLavTLK'q. "'Or 6 8 ’ dkTjdr] rd k^yopL^va Kal icTTiv dvayKoiov 
Tip TrapacrripLaLVopLivcp pLovov rd pLeyidrj t&v btacrTTipLdTcov 
30 bLaLcrOdv^crOaLy (l)av€pbv ykvoiT dv | i'nicTKO'KovpikvoLS* 
yap TLdipL€V09 crrjpLe'La t&v btacrTTipLdTcov ov Kad^ kKdcTTriv t&v 
ivvTrapypvcT&v avroLS btacpop&v tbiov TiO^Tai (rr]pL€LOVy 'olov 20 
40 el TOV bid Tecrcrdpcov TvyydvovcrLV al bL\\aLpi(r€L9 ovcrai 
TTkeiovs as 'noiovcriv al t&v yev&v biac^opaiy rj o^rjpiaTa 
TrkeLova TTOLel rj ttjs t&v dcrwOeTcov bLacrTTjpidTcov Td^ecos 
5 dkkoLcocTLS* TOV ovTov be koyov I KoX Trepl t&v bvvdpiecov 
epovpiev as al t&v TeTpayopbcov c^vcreis TroLovcrty to ydp 25 

3 TOV ex rh Mb 4 t^p supra lin. add. Mb 7 diafiaprr)- 

k6tos B a\rjd€s post y^p add. H ov post Sri add. Mar- 

quard 9 yptiil/aadai^ y^p a\f/aa’dai R ii rhp^ rb M V S 

fi€Tpop . . . iapLpiKSp restituit Marquard 14 Kal Hpiard yc 

cidcpai in marg. Me (?) R Kal post iari add. H 17 ex 

rh Mb fidpcp B 20 xmapxovaSiv H : ipvnapxovffap ex 

ipvirapxdprap Ma avrois supra lin. add. Me 21 ei in ras. Mb 

^id supra lin. add. Me : om. V B in marg. 3ia rca’O’dpapl 8' S 

23 & post irK^lova add. Marquard ^ R avvQirccv E 

24 \6y($)v S 




V 7 r€pfioXaLcov koX vrjT&v Kal pL^crcov Kal VTrarQv t& avT& ypd-- 
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§€ pLTjbev. "'Otl 8’ ovb€V icrn pL€pos rrjs crvpLTrdcrrjs ^vvecreoos to 
5 biaio- 0 dr€o- 0 ai t&v pL^y^O&v avr&v, €\€\dri pL€V ttoos Kal iv 
dpxfi) pdbiov I b\ KOLi €#c T&v pr\ 6 r\(TopLiv(ov crvvib^iv* ovre yap 15 
ray r&v r^rpayopbcov ovre ray rSiv (pdoyycov bvvdpL€LS ovre ray 
T&v y€V&v btacpopds ovt€, a 7 r\&s t^v tov crvvOiTov 

Kal Trjv TOV do‘vv\ 6 €Tov biacpopav ovt€ to cuttKovv Kal /xera- 20 
10 / 3 oAr)z; €\ov ovt€ tovs t&v pL€\o 7 rou&v Tpoirovs ovt dXXo 
ovbivy &(TavT(os €l 7 r€LVy bi avT&v t&v pL^y^O&v yiyv^Tai 
yv&pLpLov. Et piev ovv bt dyvoiav t^v v' 7 r 6 \Kri\lnv TavTTjv 25 
iayrjKao'Lv oi Ka\ovpL€VOL appLOViKoi, to pkv ^Oos ovk av etev 
aroTTOt, TTjv b€ ayvoiav iayypdv Tiva koX pLeydKrjV eTvat Trap’ 

15 avTois dvayKalov* €t be avvop&VTeSy otl ovk | eon to irapa- 30 
(rqpLaiveaOai Trepan r^y eipr\pLev 7 ]S €7rt<rr77p.rjy, yapi^opievoi be 
roty ibi&TaLS Kal TreLp&pievoL dnobibovai dcpOaXpLoetbes tl 
epyov TavTTjv eKTedetKao-L t^v VTrdXrjxl/LVy pieydXrjv || {dv) 41 
aS 0 ty avT&v aTOTriav tov TpoTrov KaTayvoirjv Trp&Tov pieVy 
20 OTL KpLTrjv OLOvTat beXv KaTacrKevd^eiv t&v eTnaTrjpL&v tov 
I bL&Trjv —aroTToy yap dv | €?rj ro avro piavOdvcov Te koX 5 
KpivLov 6 avTos —, eTteiGi* otl {irepas) tov ^vvLevaL TLOevTes 

I vircpPoKalcov Kal vrjTwv Kal fiiatav Kal vnarav conieci xnr^p- 

fioKaiuiv Kal vr}Toov] rrjs ^Tr^pfioKaias H : {m^pfioKaias vijTrjs B : vir^p- 
poKaias Kal j/iirrjs R: ^•n^pfioKaias rell. (in marg. B) fi 4 ffci>v 

Kal ^Trarav] fji4(r7js Kal virdryjs codd. 2 ^lopi^^i rh Marquard : 

^iopi(€Tai codd. 3 arifjL^itp R Sxrr^ restituit Marquard 

6 TOV prjdrja’OfA4i/ov H rd Kara post yap add. Westphal 

8 d)s ante avKas add. H r^v R: rell. tov <tvvQ 4 tov 

Meibom : t 5 )v <TvvQ 4 T(av codd. 9 kolL t 5 )v a<TvvQ 4 T($)v biatpopiLs 

H 10 oih‘€ a corr. suprascr. B fi^KoiroiXSiv V: fi^Kovoiav 

rell. 12 yvapifxav B di Hyvoiav^ hiivoiav H 14 Se] 

H 17 Idiorais S d'Kodovvai H 6<pda\pL0€id€<rrt Ma: 

accent, acut. supra 6 alterum, et t supra <r add. Me 18 4Kr€64iKa(ri 
S H tiv restituit Marquard 19 KaTayvoiTfv] v 

add. Mb 21 idiSrrjv S 22 Tr 4 pas restituit Marquard tov] 

TO MVSB: om. R 


K 2 



(pavepov Ti ipyov wy oXovrai avai^aXiv riO^acnv* Travros yap 
lo 6 (p 6 akpLO(pavovs ipyov nipas icrrlv fj ^vv^ais. | to yap iiri- 
crrarovv iiacn koX Kplvov tovt earr [^] ray (Se) xeXpas ^ 
Trjv (fxov^v rj to (rro/xa ^ to irv^vpia [17] oorty oUTai ttoXv tl 
15 biacpipeLV t&v a^xcov opydvcov ovk opO&s biavoelTar | €t §€ 5 
TTjv xpvxv^ T^ov KaTabebvKos kcTTiv fj ^vv^cris Kal /xr) 'npox^^pov 
pLTjbe TOLS TToAAoty (pavepov, KaOa/n^p aX T€ 

20 ra AotTra t&v tolovtcov, ov bta tovto aAAcoy V7ro|Arj7rr€oi; 
€X€tz; ra eipripL€va. 8trj/xaprrj#c€z;at yap (TvpL^rjcr^Tai roArj- 
dovSy iav TO pL€V Kplvov /xTjre Trepan pLriT€ Kvpiov 7 roto)/x€z;, ro 10 
25 b\ KpLv6pL€Vov KVpLov T€ Kal 'nipas. Ovx be | cart 

TavTTjs fj Trepl rovy av\ov9 V7roArj\/rty aroTroy pLeytaTov 
pLev ovv Kal KaOokov pLokicrTa {aToirov) tQv apLapTrjpLdTcov 
ecTTl TO €ty opyavov dvdyeiv Trjv tov ^ppLoapievov (pvaLV bt 
30 ovbev yap t&v | roty opydvoLS VTrapxdvTcov tolovtov €<rrt ro 15 
rjppLocrpLevov ovbe TOLavTTjv Td^iv ^xov. ov ydp, otl 6 avAoy 
TpVTTTjpLaTd T€ Kal KOLktas Ix^t Kal ra koLira t&v tolovtcov, 

42 OTL be x^^P^^Py^^^ 11 T&v x^^P^^ 

T&v koLTT&v piep&v OLS eTTiTeiveiv Te Kal dvievai TrecpvKe, bta 
5 roiJro (rypLCpcovel bid Teacrdpcov rj bid TrevTe i]Tol bid 7ra\(r&Vy 20 
7] T&v dkkcov bLaaTTjpidTcov eKacTTov kapifidvet to TrpocrrjKov 
pieyeOos. IIdvT(ov ydp tovtlov VTrapxdvTcov ovbev tjttov ra 
piev TrkeLO) biapLapTdvovaLV ol avkrjTal Trjs tov rjppiocrpLevov 
10 ra^ecoy, oAtjya 8’ eorlv a Tvyxdvovcri noiovvTes irdvTa raSra, 

Kal ydp acpaLpovvTes Kal Trapa^dkkovres Kal t& TTvevpiaTL 25 

3 Tra<ri post iiriffrarovv ponit H Kplvav H fj seclusi : in ras. 

Mb 56 addidi 4 fj seclusi Sans S B : *6 tis ex elf ns (ut 

vid.) Mb : 3 ns cum macula post ^ VR 5 ^ia^ 4 p^iv Marquard 

H : dia<l)€p€i rell. 6 KaTad€dvK6s Meibom : Kara^^dvKdas codd. 

12 avKobs Meibom : dWovs codd. 13 ^tottov restituit Marquard 

14 om. H 15 Tap toTs opydvois in ras. Mb rb om. H 

16 ToiavTTiv] ravTtjp H 17 rds ante Koi\las add. H 18 ^ 

av\rjT^s ante Marquard t^p /i€p] rbp flip B 

20 rh ante did Tca’O’dpap add. H S rh did irepr^ fj rh did Traircop H 

21 Kafifidprj R 23 av\7)Tal] av\ol S 24 & supra lin. add. 

Mb iTriTvyxdpovffi B (pv e corn) R 25 ry ttFI S 




€7nT€LVOVT€S Kal aVL€VT€9 Kttt TOLS aXXatS alriaLS iv€pyOVVT€9. 
axTT etvaL | (^av^povy on ovbev bLa(l)€p€L to koX&s iv 

TOLS avkOLS TOV KaK^is* OVK iSet §€ TOVTO (rvpL^aLV€LVy €L7r€p 
TL 6 (I)€\os Trjs €ty opyavov tov rjppLOcrpLivov avaryooyrjsy 
5 bX)C a/xa r’ els | tovs avkovs avrjyOai to piekos Kal evOvs 
aaTpa^es eXvai koX avapLapTr]Tov koI opOov. akka yap ovt 
avkol ovTe tQv akkcov ovdev opyavcov TroTe ^e^aidicreL Ttjv 
TOV fippLoapievov (l)V(rLV Ta^tv | ydp Tiva Kadokov Trjs <^iJ<r€a)y 
TOV rippLoapievov davpLaoTrjv pLeTakapL^dvet t&v opydvcov 
lo eKacTTov bcrov bvvaTaiy Trjs alaOrjcrecos avrols imaTa- 
Tovcrrjs rrpbs rjv dvdyeTai Kal Tavra Kal ra koLTra | t&v KaTa 
pLovcriKTiv. Et i^e) ns oceToi, otl tcl TpvmjpiaTa opa Tavra 
kKd<TTr]s r\pApas ^ ras xopbas ivrerapLevas rds avrdsy bta 
tov 9^ evprjcreLV rb rippLoapievov iv avrols biapievov re koX ttjv 
avrrjv rd^Lv bLacr&C^Vy 7rav\\T€k(jis evri6r\s* &(nrep yap iv 
rals xppbals ovk ecrn rb rjppLocrpLevoVy idv pJj ns avrb bta 
Trjs yeLpovpyias irpocrayaycvv dp/xoVrjrat, ovtcos ovbe iv rols | 
Tpv7rripLa(rLVy idv pufj ns avrb yeLpovpyta 7rpoa‘ayayci)V dp/xo- 
(TrjTaL. on 8’ ovbev r&v opydvcov avrb appLorreraL akka fj 
2 0 atadriaLS iortv rj tovtov Kvpia, bfjkov on ovbe koyov belraty 
(l)avepbv ydp. | &avpLao‘Tbv 8’ el /xrj8’ els ra roLavra jSAe- 
TTOvres dcfTLOTavrat rrjs TOLavrqs V7rokrj\lreoi)S bpQvres on 








I Kal avUvr^s H Kal roiy] reus R 3 KaKcos^ 

Ka\as B: om. R tovto] rb M R : rod S 4 eis Spryavov rod 

^pfiofffiivov Meibom : eis rh ^pfioa/iivov 6pyavov codd. 5 /idXos H 

6 aarpaPhs ex aarpapisi deinde 2 litt. eras. Mb: atrrpapks •re B 

7 d\\a)v in ras. Mb ovdhv post opydvosv ponit H 8 ^pfioafikvov 

(pitaiv* ra^iv ydp riva KadoKov rrjs (pvaeas rod (ante rod ras ) in marg. 
Mb : (pTLfO’u/ (^om. Kal sed supra lin. add.) ydp rijs KadoXov <^v(r6a>s (t^s 
in ras. in qua riva vel Tis erat, ante (pva^eas 3 litt. eras.) Vb : item B 
sed in marg. rd^iv ut scripturae discrepantia pro (p^taiv : rd^iv* Kcd 
ydp rrjs KaddXov <l)V(r€($)S S 10 ante 4<t} 4 litt. eras. M ovtois ] 

avrrjs B iTnrarTOTLfa’Tis R 12 ei] eis B 56 restituit Marquard 
(leg. H) ravra M V B S 13 ^ M V S B 14 t€ om. R 
15 avr^v om. H hiaffdo^eav Ma : ^laaSi^ov Mb rell. 16 ^id rrjs 

om. R, supra lin. add. Mb 17 ^ app. 6 (T^iTai {tj 

suprascr.) B oifras . . . apfidcTfrai om. H 19 rav om. H 

20 fAvpia {kv supra fiv scr.) H oih^ H \6yov B H 











KLVovvrat ol avXol Kal ovbeTToO^ oxravroos ^yovcriv oKTC eKacrra 
T&v avkovfievodv fi^ra^AWeb | {Kara) ras alrias a<p^ &v 
avK^irau ^^ebov 8r) (^av^povy on bC ovb^fiLav airiav €ty 
Tovs avKovs avaKriov to /xeAoy, ovr^ yap ^^^aidicr^L rrjv 
Tov fippLoapievov tcl^lv [to elprjpievov] opyavov ovt\ €t rty | 5 
(^rjOrj b€LV €ts opyavov n noi^icrOai Trjv avayayy/jv, €ty rovy 
avXovs ^v TTOLTireoVy iTr^Lbrj pLoKicTTa irkavaraL Kal Kara r^v 
avXoTTodav Kal Kara r^v yjeipovpylav Kal Kara rrjV Ibtav 
(l)V(rLV. I 

pL€V ovv TrpobUXOoL ns av Trepl rrjs apfjLovLKrjs KaXov- 10 
[jLevris TTpay [Mare ias cryebov kern ravra* fikWovras 8’ km- 
yjEipeiv rfj mpl ra aroixeLa 'npaypLareia bn TrpobLavorjOfjvaL 
ra TOL\ab€* on ovk kvbkyerat KaX&s avrrjv bie^eXOeLV /xr) 
TTpov 7 rap^dvT(ov rpt&v r&v prjOrjo-oixkvcov Trp&rov pikv avr&v 
T&v (^aivopikvoiv Kak&s \r](p 9 kvT(oVy kmira bLopLcrOkvrcov kv 
aVTOLS T&v 11 T€ TTpOTepCOV Kal T&v VCTTepCOV OpO&Sy TpLTOV bk 
TOV (Tvpi^aivovTos T€ Kal ofjLoXoyovpLkvov KaTa Tpoirov ervv- 
oipOkvTos* *E7r€t be irdaris eTrtoTTj/xrjy, rj tls €#c 7rpojSArj|/xdra)z; 
TrXeLovcov (TVvk(TTy\KeVy dpyas TrpoarjKov kon Kafieiv k^ &v 
b€i\ 6 ri(r€TaL rd /xerd tcls dpydsy dvayKalov av eir\ XapL^dveiv 20 
'npoerkypvTas bvo ToXerbe* Trp&Tov piev ottoos dXrjOks T€ Kal | 
(^aivopievov eKaerTov ecTTai t&v dpxpeib&v TrpojSArj/xdrcoz;, 
€77660’ 0770)9 TOLOVTOV oloV kv TTp&TOLS V 770 TTJS alcrOrjaeCOS 
avvopdo-OaL t&v ttjs apfiovLKrjs TTpayp^aTeias [xep&v to ydp 
770)9 diraLTovv aTTobei^Lv | ovk eerTLV apyoetbes. KaOoXov 25 
8’ kv T& apyeadaL 77aparrjprjr€oz;, 0770)9 /xtjt’ els tt/v 
VT repopiav kfimirTcopLev Atto tlvos (jxovrjs 17 KLvrjcreoos dkpos 

I post avKol unum verbum eras. M 2 /corefc restituit Meibom 

3 5))] 56 H 4 fii\os H S rh clpTjfikt/ov seclusi cl om. 

M V B S 6 aycoyijv M V S R H 7 %v ex ?iv Mb : %v 

V S B, H (ante els rebs) 8 koI Karh r^v xct^oi/pyW in marg. Mb 

10 irpocKdoi B in marg, 17 rhv ante rpSirov add. MVSB 

a’vva<i>d€VTos H 18 cirel ex iirl Mb 19 TTpoccxoi^Ta H 

24 fiirpoiv H 25 TTws S wncTovv H 26 t^v om. V S 

27 ifjLTri'moifjLcv^ lac. irrccfiev R : ip/nliTTopLcv H ^ cbnieci: ^ codd. 




ap\6fjL€V0L9 \ky\T av KapLTrrovr^s kvros 7 ro\|Aa t&v oIk^lcov 20 
a 7 ToXLfJL 7 rdv 0 i)ll€V . 

Tp(a yeirq r&v pL€kcobovpL€V(»)V kcrrlv* hidrovov xp&pLa 
5 dppLOvia. at pL€V obv biatpopal tovtcov ^crrepov priOrjcrovrar 
TovTo 8’ avTo €#c#c€t(r 0 a), on ttclv | /xeAoy €<rrat rjrot bidrovov 25 
7) xpaypLarLKov rj ivapfidvLov rj pllktov €k tovt(ov rj koivov 


A^xrrepa 8’ iarl btaLpecTLS r&v bLao’TqpLdrcov ^Xvai rd pikv 
10 (rdfjLcIxova ra | be bidipiiiva. yvoDpipLiararai fxiv boKovcnv elvat 30 
avrat bvo r&v 8ta(rrrj/xart#c£z; btatpop&Vy 17 re pieyeOeL bia- 
(pepovatv dWrj\(»)v Kal 17 ra (r6pL(pOi)va r&v bLacfxovcov TrepU- 
XeraL 8’ fj vcrrepa p7]del(Ta || btaipopd rfj TTporepa, ttclv yap 45 
(rvpL<p(ovov TravTos bLacfxovov btaipepeL pLeyeOet. ’EttcI be r&v 
15 avpLcjxovLov 7r\eLovs elcrl Trpos aWrjXa 8ta<^opat, /xta rty fj | 
yvLopLpLLordrri avr&v eKKeiaQo) (TrpcSrrj)* avrrj 8’ ecrrlv 17 fcara 5 
pLeye6o9. "^Eoro) 8r) r&v (rvpLcIxovcov ofcro) pLeyeOrj* eX&x^o'Tov 
piev TO bid recrcrdpiov — crvpi^aLveL be tovto {avrfj) rfj tov 
(jxeXovs!) (pvcreL eddx^^crrov eXvar crTjpLeLov be | to pieXiobeLV 10 
20 piev fjp^LS TToWd TOV bid Tecrcrdpoov ekdTTO), irdvTa pievroL 
bLdcfxova —. bewepov be to bid iriirre, o tl 8’ dv tovtcov 

dvd pLecrov 17 pieyeOos ttclv lorat bidtpLovov. TpiTov (8’) eK 
T&v eipr]pLe\V(i>v avpLcjxovcov crvvdeTov to bid Tracr&v, Td be 15 

4 Mb in marg. apxh Vb in marg. irSaa yevTj fxeKcpdias iariv ins. 

Mb : om. R 5 apfiovioi] vid. fuisse apfioviav M 6 fidKos H 

^ Tu\ ex *6 T€ Ma (b ?) 7 e/c om. M V B R S 9 iffrXv post 

^lourTtifiirav ponit H post iarl una litt. eras., vid. fuisse iffrlv M 
12 ^loup^vdiv ex ^ia<popSov Ma 13 ei' ante tt) add. H 14 iravros 
om. et ficycdci ante ^ia<l>(avov ponit H opa Ilop<l)vpioi/ iv rip els 

^ApfioviKa TOV TlroKcfiaiov {fTrofjLvfifjLori in marg. H 16 Trp<$>Trj 

restituit Marquard, sed ante iKKclcBa) ponit 18 (rvfiPcPrjKc H 

avrf) restituit Westphal rf) om. B tov B : avrov M V S R : 

a^ov H 19 fi€\ovs restituit Westphal 20 ttoAA^ om. R 

22 ava fi€<ra)v B cffTai H : cTvai rell. post cJvai add. Aeyo/iev 

Marquard 5’ restituit Marquard 23 avvT^Qev H 




TOVTcov ava fiecrov bLdcfxova ecrraL. Tavra fiiv ovv kiyofiev 
h irapa r&v ^impocrOev 7rap€t\77<^a/x€z;, Trepl h\ r&v Xoltt&v 
20 fl/UV aVTois bL0pL(TT€0V. | Up&TOV pL€V OVV X€KT€0V, OTL TTpOS 
T& bia TtacrSiV ttclv (rvpL<p(ji)Vov 'npocrriQip.^vov bidcrTTipLa to 
yiyv 6 pL€Vov avr&v /x€y€0oy oijpLcIxovov Trotet. #cal icrriv 5 
25 Xbiov TOVTO TO TrdOos Tov crvpLcIxovov I TovTOVy Kal yap eXar- 
Tovos TTpoaTeOevTOs Kal Xcrov koX pi^i^ovos to yiyvopL^vov €#c 
Tr]s crvvOicr^oiS avpLipoovov yiyv^Tai* tols be TrpcSroty cn;/x- 
(jxivoLs ov (Tvpi^aiveL TovTOy ovT€ yap to Xcrov cKaTcpco 
30 av\T(av crvvTeOev to oKov crypapcovov ttolcl ovtc to cKa- 10 
Tepov avT&v Kal tov bid Tracr&v crvyKeipievoVy dX)C del 
btaipcovricreL to eK tS>v elprjpLevcov crv/xclxoviov crvyKeipievov. 

46 Toz;o 5 8’ ecTTlv w to bid irevTe || tov bid Tecrcrdpiov piei^ov* 

TO be bid Tecrcrdpiov bvo tovcov Kal ripLicreos. T&v be tov 
Tovov pLepQv pLekcobeiTai to rjpLicrvy b KaXeiTai fjpLiTovioVy Kal 15 
5 TO TpiTov pieposy I o KakeiTai biecris xpiopiaTiKri ekaxicrTrjy 
Kal TO TeTapToVy o KakeiTai biecris evappLOvios ekaxicrTr]* 
TOVTOV 8’ ekaTTov ovbev fiekcobeiTai bidcrTrjpia. Aei be 
10 TTp&Tov piev TOVTO avTo piT] dyvoeiVy otl | irokkol r/8rj 8 t 7 j- 
piapTov VTToka^ovTes fipids keyeiv oti 6 t6vo9 els (rpta rj) 20 
Tecrcrapa Xcra biaipovpievos piekcobeiTaL, crvvel^Ti 8’ avTOis 
TOVTO irapd to pir} KaTavoeiv oti eTepov ecrTi to Te ka^eiv 
15 TpiTov pLe\pos TOVOV Kal TO biekovTa els Tpia tovov pLekiobeiv. 
eireiTa aTrAcSy piev ovOev virokapL^dvop^ev elvai bidcrTripia 
ekd^icTTOv. 25 

I ai'ek fiiffosv H ^liiptava cJvai \cy 6 fjLcv. Tavra fihv oiv irapa 

Marquard (5. e. \ey 6 fjL€va r. fx. 0. tt. Porphyrius) carat H : clvai 
rell. 3 fjLcv supra lin. add. Mb 4 ry] rb S H B in marg. 

5 Troiclrai H 7 fjtcyidovs post fici^ovos add. H yiyv 6 ficvov 

Marquard : \cy 6 picvov codd. : ycvoficvov Porphyrius 9 ov supra 

lin. add. Mb irddos post rovro add. H ii 51 s rcdci/ros post 

avrSov add. Meibom oel Zia<p(avi)<Tct\ rj ^ia<pd>v7i<Tis M V B S : ^ 
dia<p(avri<ris R 13 toO] Kal R 14 B H IT Kal 

. . . iKaxio-rri om. H b R : om. rell. 20 viroKafidvrcs ex 

\nro\afi 6 vras Mb rpla ^ restituit Marquard 2r avroTs post 

rovro ponit H 24 circid* airKas S 




At bi T&v y€v&v bLa(l)opal \afifid\vovTaL iv Terpaxppbco 

TOLOVTCD olov icTTL TO (2770 pLi<Tr]S €</)’ VTTdT 7 ]Vy T&V pL€V OLKpOdV 
pL€v 6 vT(OVy T&V §€ pL^aCOV KLVOVpL€VOi)V 076 pi€V dpL(l) 0 T€pCOV 

076 §€ Oaripov, ’EttcI 8 ’ avayKOLov rov KLVov\pL€Vov (p66y- 
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7rot€t 8’ avTr] bidrovov ykvoSy ^apvrdrr] 8’ 7] bCrovov, yiyv^rai 
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15 TdcTLV dcpLKcovTat ij 7 € Xt^az/oy dvLepikvri fcat fj TrapvTrdTrj 
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20 bLao-TrjpidTLov 8ta tl yap pikcrqs pikv fcat 7rapa/x€07j9 kv koTL 
bLdaTTjpLa fcat TrdkLV av pikcrrjs T€ Kal VTrdTrjs fcat t&v akk(s>v 
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bLacTTipLaTa TTokkd 0€7eoz; €tz;af Kp€LTTov yap t&v (pOoyycov 








2 rav supra lin. add. Mb 3 Se supra lin. add. Mb; om. B 

56 fiiaosy H : fiiaosy Bk rell. kfiiporipuiv ex afiiporkpov (ut vid.) Mb 

4 eTrei 5* &i' M : ivciBav V B S 5 ArjTTTeos] rkos corn Mb 

6 €KaT€pov Marquard : cKarkpav codd. 5))] /i)) B 8 aBrri H : 

avrrj M V B S : avr^ R fiapvrdrrj 8k ^ 8 ( in ras. Mb rj om. S 
10 Koi virirrjs restituit Marquard ii cKarrov Me in marg. B : 

ixirrovi Ma V S B on om. R 12 roTorav post ‘travreov add. H 

15 Too’ii'] rd^iv H fj TrapvTrdrrj] {nrapwdrri B 16 6 piC€<rdai 

Marquard ; apl<rdai R : 6 pl<rdai in marg. B : Spiciadai rell. 0 om. H 
17 oTi . . . davfid^ovffi restituit Studemund 19 KiviQkvros B : 

TcdkvTos Marquard 20 irapafiiffris ex irapafiiffov Me : irapafieffov 

V S : iraph, fikaov B 21 aS ex av\o\ (\ol eras.) Mb kol Bwdrrjs 

om. in marg. B 22 restituit Meibom Kivovvrai R : Kivovai 

ex K€ivov<ri (ut vid.) Mb : Kivovai rell. 




ra ovofiara klv€lv fiTjKeTL Kakovvras kL^avovs ras AoiTray, 
iireibav rj btrovos {ki^civos:) KkrjOfj rj r&v aXX(ov /xta ijns 
20 TTOT ovv. b€LV ycLp | kv^povs ^Xvai (fyOoyyovs rovs to €T€pov 
pL€y€6o9 opL^ovras* be belv ^xeiv Kal ra clvtl- 

CTpeipovra. ra yap Xcra rGiV pieyeO&v roXs avroXs ovopLaai 5 
25 TrepLkrjlTTTeov eXvai. Ilpoy brj ravra tolovtol tlv€ 9 ikexOrjo'av 
\6yor irp&Tov piev on to a^Lovv tov 9 biatpepovTas akXrikcov 
ipOoyyovs tbiov pieyeOos ^xnv biacTTripiaTos p^eya tl KiveXv 
30 icTiv op&pLev yap | otl vi^tt] piev Kal pLearj TrapavriTris Kal 
Xi^avov btacfyepeL #cara t^v bvvapnv Kal ttoXiv av TrapavrjTri 10 
T€ Kal kLxavos TpiTTjs T€ Kal TTapvTraTT]9, &(ravT(09 be Kal 
48 ovTOL TrapapLearjs Te Kal viraTij^—Kal bia TavTTjv || ttjv ahiav 
ibia KeXTai ovopiaTa eKacrTois avT&v—, biacTTqpLa 8 ’ avToXs 
TraoTLV VTTOKeLTaL eVy to bta TrevTe, coafl’ otl piev ovx oXov t 
5 ael Trj t&v <f)96yy(ov 8ia|</)opa rrjz; t&v biacrTripLaTLK&v pieye- 15 
O&v btaipopav aKokovOeXv (pavepov. "'Otl 8’ ov8€ TovvavTiov 
CLKokovOeXv OeTeoVy KaTavorjaeiev av tls €#c t&v priOrjcopLevcov. 

10 ripairoz; piev ovv el Kal #ca0’ €#ca|(rrrjz; av^rjCLV Te Kal ekaT- 
Tcoartv T&v Trepl to ttvkvov yLyvopievoov Xbta ^r]Tr\(TopLev ovo- 
/xara, brjkov otl aireipLov ovopiaTcov berjo-opLeOa, eTreLbrjirep 6 20 
49- 7 kL^civov roTToy eU aTreipovs TepLveraL ro/xay. \ akrjO&s 
yap TLVL av tl 9 irpoaOeXTo t&v apLtpLal^riTovvTLov irepl ray t&v 
10 yev&v I y^P '^pos ttjv avT^v bLaipecTLV fike- 

I TO add. Mb 2 ^ codd.: fj ^ Marquard Blrrovos R 

\iXo>vhs addidi: ofira Marquard ijns renovat Mb accent, add. Me : 
TjTis cum ras. supra lin. V 3 BeTv Marquard ; dcT codd. rh om. S 
4 56? H 5 yhp l<ra Studemund : iripiaa codd. : 5’ ?<ro Marquard 

6 ToiovToi^ oJtTol H eAex^Tyo’oi'] 4 in ras. Me (?) 9 ‘jrapavifTTjs 

ex irapauiiTrjv Mb 10 6 * post iraXiv add. H ii TrapvTrirris^ 

vTrdrrfs R 12 v'lrdrrjs'} v 4 )rris H 13 avrSiv supra lin. add. 

corr. B 14 ei', rh conieci : 4 v ry codd. 15 hiaa’rrjfjLdrap H 

17 aKoKovQ^LV dcTcov conieci: a.KoXovd'qriov codd. 18 ei #col] /col 

om. H iXdrroffiv S 19 (yiTi)(T(afjL€v M V S B 20 $677(rJ/i60o] 
if](T 6 in ras. Vb 21 rc/jLvcrai post rofids ponit H oos 

dXridas . . . diaip 4 (r€a)i/ legg. in codd. post hiafiiv^iv in p. 140, 1. i : 
ordinem niutavi 22 irpoadcTro ex ‘irpoo’doTro Me: ‘irpoa’doTro VBS 

dfi<l>ia’firjTovT(av (y suprascr.) B 



TrovT€S 7 rdvT€s ovT€ TO XpS/xa ovT€ T^v ap\koviav dpiioTTovraiy 
&(TT€ TL [mclWov t^v biTovov Aixaz/oz/ k^Kriov rj t^v iiiKpUd 
awTovayr^pav; ap\pLOVLa /xa; yap etvaL Trj aicrOricr^L Kar 
dpaporepas ras bLaLpicr^LS (paiveraL, ra be pieyeOr] r&v Siaorrj- 
5 pidrayv brjkov on ov ravra iv eKarepa r&v biaipecreoiv. | 
eTTeira TreipcipLevoL Traparripeiv to t Xcrov Kal to avLcrov diro- 
^akovpLev Trjv tov opioCov T€ Kal dvopLoiov bidyvcocnv, ScrTe 
pLTjbe TTVKVov Kaketv l£a) kvbs pieyeOovs, brjkov 8’ otl pLTjb^ 
dppLoviav pLTjbe xpCipLa, tottw | ydp tlvl Kal Tavra Swopiorai. 
10 Arjkov 8’ OTL ovbev tovtoov icrTi Trpbs T 7 ]v ttj^ alaOrjaecos 
(pavTacrtav eKeivr\ piev ydp els o/xotorrjra evos tlvos etbovs 
j^keTTovaa to Te yjpiapLa | keyei koX ttjv dppLoviav dAA’ 
ovK els evos tlvos bLaorqpiaTos pieyeOos, keyo) be ttukvov 
piev elbos TLOeXcra e(os dv rd bvo bLaoTrjpLaTa tov evos 
15 eAdrro) tottov KaTeyrj — epicpaiveTaL ydp ev TraaL toXs | ttvk- 

XP<opLaTos be eXbos ecos dv to yjpo^pLaTLKov ^6os epLcpaivtiTaL. 
Ibiav ydp brj KLvrjaLV eKaaTov t&v yev&v KLveXTaL irpos ttjv 
ataOrjaLV ov || pLLa yjxopievov TeTpayppbov bLaLpecreL dkkd 
20 TTokkaXs. (2(rr’ etvaL <pavep6v, otl KLVovpieviov t&v pieyeO&v 
(TupL^aiveL (jxeveLv) to yevos, ov ydp opLOLcos KLvelTaL t&v 
pLe\ye9&v KLVovpLev(ov p^expi^ tlvos, dkkd bLapieveL* tovtov be 




2 post add. ov iriw pt^diop ffwidcTp Marquard hiTovov conieci : 
Bidropop codd. ^ H 3 apfiovlas sed os postea corr. B 

4 fjLcycdT) post BiaCTrifidTav ponit H 5 tovto M V B S 8 drjXop 
5* on om. et fiijd* pro fjLtiB' scrib. Marquard d’ S : om. rell. ii ydp 
om. VS 12 fixiiroyffa in ras. Ma 13 ovk els ephs renov. 

Mb els om. B elclp d>s R iruKPovfiep B 14 etbos in 

marg. Mb : eUBovs MVS post elSos add. orap fj (pap^ (papfj rd 5 io- 
(TriifjLaTa ofiroo Marquard TeQe'io'a M V S B eoos conieci : dts codd. 

(5io)<rT^/AOTo TOV erat in ras. deinde renov. Mb 15 Korex^ip 

H ep TTocri toTs renov. Mb 16 (/cofVep dplffap renov. Mb 

17 $6 el^os ea)s conieci : Be ^ dieceas R : dei dieceas rell. {Bieffeas in 
ras. Mb) dp rh XP^ Mb ejKpalpTjrai Marquard : e/Kpalperai 

codd. 18 Idla S Klp7j<rip^ heiKPVffip R i^Kip^eirai irphs t^p 

in ras. Mb 19 ^ in ras. Mb diaipe<rei ex dialpenp Mb 

21 fiepeip addidi : tovtop elpai Marquard ov in ras. Mb 22 Sio- 
fiepei renov. Mb 




fi€V0VT09 elKos Ka\ ras r&v (pOoyyayv bvvdfi€LS bLafi€V€LV. to 
20 ydp €Lbo9 Tov T€Tpaxppbov ravjro, bt oTrep Kal rovs r&v 
bLaarrjpLdroiiv opovs dvayKoiov elTT^'iv rovs avrovs. KafloAoi; 

8 ’ elire'LV, ecoy &v p^ivip ra r&v TrepL^xovrcov ovopLara Kal 
25 XeyqraL avr&v f) piev o^vrepa pL^ar] VTrdrr] 8’ f] | l 3 apvT€pa, 5 
btapLev^'i Kal ra r&v irepL^xopi^vcov ovopLara Kal prjOrjcreTaL 
avT&v 7 } pL€V o^ripa Xiyavos f) be ^apvrepa TrapVTrdTrj, del 
yap TOV 9 piera^v pLearis re Kal VTrarrjy Kiyavov re koX nap- 
30 vTrdrrjv (rj) aicrOrjlcrLS TLOrjcnv. To 8’ d^Lovv 17 ra taa 8ia- 
(TTqpLara roXs avroXs ovopLaacv dptCeaQaL rj ra dvLcra erepoLS 10 
/xax€(r 0 ai roXs (patvopievoLS eari* to [re] yap VTrarrjy Kal 
TrapvTrdTTjs r 5 T:apvTrdTr\s [TrXeovdKis icrov pLeXcobeXvai rj] 

50 (fcal) \L)(avov || pLeXiobeXraL Trore Xcrov Trore dvicrov* bn 8’ 
ovK evbexerai bvo bLaaTrjpLdTcov e^rjs Keipievcov T 0 X 9 avroXs 
5 ovopLacnv eKdrepov avr&v (pavepov, \ eiTrep /xrj 15 

pieWoL 6 pLeaos bvo e^eiv ovopLara. Arjkov be Kal e7rl tQv 
dviacov ro droTTov* ov yap bvvarbv btapLevovros roS erepov 
tQv ovopLdroov ro erepov KLveXaOaL, irpbs aAArjAa yap AeAe- 
10 KTar I [coo’Trep yap 6 rerapros dirb rrjs pLearjs VTrdrr] Trpoy 
pLeariv XeyeraL, ovrcos 6 exppLevos rrjs pLearjs Xl^clvos Trpbs 20 
pLecrrjv Aeyerai.j Upbs pLev (pvv ravrriv) r^v biarropiav 
rocravra eiprjcrdoi. 

2 yap conieci : 5 ’ codd. elSos ex ol 5 os Ma 4 S H 

5 XiyriraC] y€vr}Tai H vvdrrj 3* ri ffapvrepa^ vTrdrrj in ras. Mb dk 
supra iin. add. Me ri om. M 5’ ^ om. V S B ^5^ fiapvrepa 
(omissis (urdrrj Se) R, in marg. B 6 Marquard : 3iafi€V€i 

codd. 7 Marquard : ficffti codd. ‘irapvTrdrrj] virdryj 

sed Trap ante v eras. M : {nrdrrj rell. 9 ^ restituit Marquard ata-Orj- 
ffiv S 10 Tois ante krcpois add. H ii fidx^t^daij a’vvcx^o'dai R 
icTi ante roiis (paivofiivois ponit H re seclusi 12 TrXfovdKis 

. . . ^ del. Meibom 13 Kal restituit Meibom Trore fx^XadcTrai 

(P supra TTore, et a supra fieXcoBcTrai scr.) Ma Trore fihv Xrrov ttotc Se 
dviaov H 14 avTois supra lin. add. corn B 17 r 5 postea 

add Ma (ut vid.) 18 Acyeroi H 19 &a’Tr€p . . • Aixoj/ 5 s Trphs 

fiiffTiv Acyeroi seclusit Marquard vrrdrris H : vrrdTti sed v post rj eras. 
M : vrrdrriv V B sed hirarT] in marg. B 20 Aeyeroi in ras. Mb : deinde 
4 litt. eras, quarum extremae roi fuisse videntur ante itphs fiiariv add. 
kolL Me 21 oZv ravrriv restituit Marquard 22 roo’oDro] rovro H 


UvKvbv §€ keyecrOd) y^ixP^ tovtov €0)9 av iv T€Tpa)( 6 pbiD 15 
bta T^crcrapodv (rvpLcjxovovvToov r&v aKpcov ra bvo bLacrr'QpLara 
(TVVT^Qivrd rov kvos ikarra) tottov Kariyrj. T^rpayopbov 
bi €l(n 8t|atp€(r€t9 i^aCperoi t€ koX yvdpLpLOL aZrai at elcrtv 20 
5 €69 yvdpLpLa biaipovpL^vai pieyeOr] bLacrrrjpLdrayv. Mia pL€V obv 
{rovrayv) r&v biaipicr^iav kcrriv kvappLOvios iv jf to pikv ttvkvov 
ripLLTovLov icrri to | b\ koi'nov biTovov. rp €69 b\ xpcopLaTLKaC, 25 
ij T€ Tov pLakaKov yjpidpiaTos koX fj tov rfpLiokiov kcu t} tov 
T ovtaiov piakaKov p!kv obv yjxopiaTos icTTi btaLpecrLS iv fj to 
10 pL€V TTVKVOV €#c bvo )(pa)|/xar 6 #cd)z; biicr^oiv ikayicTTCiiV crvy- 30 
KUTaiy ro b\ koLTTOV bvo /X€rp 069 pL€Tp€LTaL, ^pLLTOVLCO pL€V 
rp 69 , xpo^piaTiK^ bi btiaeL aira^, 63 (rr€ pL^TpeLo-OaL Tpialv 
ripLLT 0 v( 0 L 9 Kal TOVOV TpLTCO /X€p€6 SlTTO^* i(TTL §€ T&V yjpOipLa- 

15 yivovs TOVTOV. rfpuokiov b\ yjpiapiaTos biaip^cris icTTiv iv 51 

17 TO T€ TTVKVOV TIpUokLOV icTTL TOV [t’] ivappLOvCoV Kal T&V 

biia^cov (€#car€pa) €#car€pa9 t&v ivappLovtcov otl 8’ iorl | 
pLei^ov ro fipaoktov ttvkvov tov piakaKov, pabiov avvibelv, 5 
ro piiv yap ivappLoviov btiaecos keLTret tovos aval to bi 
20 x/>^*>/xar 6 #crj 9 . Toviaiov b\ xpdpiaTos bialp^cris icTTiv iv 17 
ro pL€V TTVKVOV i^ r}pu\Tovi()iv bvo orvyKeLTaL to be koLTTov 10 
TpLTjpuTovLov ioTLV. /x€z; obv ravrrj 9 r ^9 bLaLpeaecos 

I tiv om. R 3 Karixn Karix^^ • /corexei S Tcrpax^p^ov 
/C.T.A.] in marg.nToA6/ia?oi^ iv ^ApfioviKoTs H 4 ante i^alperoi 

una litt. eras. M aT I Kal R 5 et yvcapi/xd iari rd diaipovficva 

ficyidrj rav diaa’rrjfidrcov H diaipovfieva MVS 6 tojjtcdv addidi 
rav om. H diaip€(r€6i)v post iari ponit H irvKvhv in ras. Mb: fiiKphv R 
7 dlTovov~\ post i litt. a eras. M 8 ^ rod rovialov] ^ rov supra lin. 

add. Mb: Tjfiiroviov R 9 odv om. R 10 Kal ante diiccav 

add. R 12 rpeis H Se add. Me : om. V B S SieVei] €i in 
ras. Mb : diiffis Va am^ &a’T€ fierpeTadai om. M V B S H fierre 
. . . a7ra| om. R rpiclv fj/xirovlois Kal t6vov rplro) fxipci in marg. Mb 
14 TTVKvav R : wKvhv rell. Aixoi'bs] os in ras. Mb 16 r* 

del. Marquard ivap/xovlov] iv add. Mb 17 eKaripa restituit 

Marquard (lac. 2 syllab. R) 19 t6vos post chai ponit H 20 dial- 

( TTVKvd 

in marg. Mb (?) Vc < ivapfiov. fioKaK. fifjiioX. 

I ^ V e' 


p€<ris^ alp add. Mx 


II. 51 

aiK^oT^poi KLvovvraL ol (pOoyyoL, fiera ravra 8* f] fikv nap- 
15 vnaTT] iJi€V€L, bL€\T]\v 6 € yap rbv avrrjs tottov^ 17 86 | Xl^clvos 
KLV€LT aL bUcTLV ivappLovLov Kal yiyv^rai to Xt^avov Kal 
vnarris bLaarripLa Xcrov r£ Xvyavov Kal /xecrrjy, cocrre /xrjfcert 
ytyvecrOaL nvKvov iv ravrr] rfi biaip^cr^u crvpi^aiv^i 8’ fi/xa 5 
20 nav^crOai to nv\Kvov crwiaTapi^vov iv Tjj t&v T^Tpaxppbcov 
biaipicr^i KotX apyecrOaL yiyvopL^vov to bi&Tovov yivos. Et(rt 
b\ bvo biaTovov btaLpicreLs, rj t€ tov piaXaKov Kal^ rj tov 
25 (TvvTovov. piaXaKov p.\v ovv icTl biaTovov 8tat|p€(rty iv fj 
TO pL€V vnaTYjs Kal TrapvTrATTjs TipuToviaiov icTTL, TO bi nap- 10 
vnaTTjs Kal Xl^clvov TpL&v biicr^oav ivappiovLoov, to be XLxavov 
Kal pLi(T 7 ]s nivTe bLeaecov crvvTovov be iv fj to piev vnaTYjs 
30 Kal na\pvndT 7 i 9 fipaTovLaioVy t&v be Xoin&v tovloXov eKaTepov 
icTTLv. Aiyavol piev ovv elcrlv e^, piCa ivappLovLos, TpeXs 
52 XpoipiaTiKoX Kal bvo biaTovoiy ocrai nep ai || t&v TeTpayppbcov 15 
biaLpeaeLSy napvnaTai be bvo iXoTTovSy Tjj yap fipLiTovLata 
XP<*)/x€ 0 a npos Te ray biaTovovs Kal npbs ttjv tov Toviaiov 
5 yjp&pLaTos biaipe\cnv* TeTTapcov 8’ ovcr&v napvnaT&v 17 p.ev 
ivappLOVLos ibia icTl Trjs appioviaSy at be TpeXs KOLval tov 
T e biaTovov Kal tov ^(pw/xaroy. TcSz; 8’ ev t& TeTpayppbio 20 
10 biacTTripLaTOdv to piev VTrarrjy | #cat napvnaTrjs t& napvndTrjs 
Kal Xixavov rj Xcrov pLeXcobeiTaL rj eXaTToVy pLeX^ov 8’ ovbe- 
noTe. OTL piev ovv Xcrov {c^avepov iK r^y ivappioviov btat- 
pecrecos Kal t&v xpcopiaTLK&Vy otl 8’ eXaTTov iK piev t&v 
btaTovcov) c^avepovy iK be t&v yjpcnpLaTiK&v ovTcns dv tls 25 
15 KaTavorjcreteVy el napvndTrjv | piev AajSot t^v tov piaXaKov 

2 avrrjs Marquard : avrrjs codd. 8 diaip€<ris diar 6 vov 

H 9 odv om. R 10 ante fjfjLiroviaiov 5 fere litt. eras, 

(vid. fuisse) M ian om. R 12 Kal in marg. Me: om. 

rell. 13 rovioLLOv ex ^fiiroviaiav Ma rovia'iov post cKdrepov 

ponit H 14 6| . . . r err apes in marg. Mb: om. R 15 * 6 <rai 

ex offa Ma 16 rrapvndrai Be rerrapes seclusit Marquard rrapv- 

rrdrrjs B : rrapvna (t' suprascr.) S Bve 7 v M : Bvolv VS 19 IBla 

H : ^Blos rell. 21 rf rrapvvdrris om. R 23 <pavepov . . . 

Biar 6 v(av restituit Westphal 




X/><o/xaroy, \Lxavbv be rrjv {rov) rovLaCov koI yap al rotavraL 
btaLpecreLS r&v twkv&v ifjLfjLekeLS (^aivovrai. to 8 ’ eKfiekes 
yevoLT av €#c rrjs evavrias Xrjxl/ecos, et | rty T:apv'naT 7 \v [lev 20 
\d^0L T^v fifiLTovLaiaVy Xl^clvov be Trjv rov fipaoXCov XP^“ 

5 fiaroSy ^ TTapv'ndrriv [lev r^v rov fipaokLov, ktyavov be r^v 
Tov fiaXaKov \p<6pLaT09* dvappLoaroL yap | (paLVovrat al 25 
TOLavrat btaLpeaeis. To be TrapvTrdrrjs Kal Ktyavov (r£ 
Klxclvov) Kal pLecrrjS Kal tcrov pLeXiobeLraL koX dvicrov d/uw^o- 
repoos" tcrov piev ev Tea crwrovcorepco bLardveoy eKaT\Tov 8’ 30 
10 ev TTOLCTL TOL9 XoLTTOLSy piet^ov 8’ oTav {tls) kiyav^ piev rfj 
crwrovcordTj] r&v btardveovy 'Trapv'TrdrTj be r&v fiapvrepcov 
TLvl rfjs fipuToviaias ypricrqTai. 

Merd be ravra beiKreov rrepl rov e$fj9 viroTV'Trcoo-avres 
Trp&Tov avTov rov || rpdrrov #ca0’ oz; d^Lcoreov to e^9 dep- 
15 opi^eLV. ^AttK&s piev ovv elrreiv fcard ttjv tov piekovs (pdenv 
CrjTTjTeov TO e^9 Kal ovx wy ol eh ttjv KaTa'7TVKV(»)\(rLV jSAe- 
TTovTes elcoOacTLv d'nobibdvai to erweyes. eKeivoi piev yap 
okiycopeLV cpaivovTai ttjs tov piekovs dycoyrjs* epavepbv 8 ’ €k 
TOV ttAtj^oo? t&v e^9 TtOepievcov btecrecoVy [ov yap 8td 
20 TocrovTcov I bvvTjOeLr] tl9 &v] p^dyjpi yap Tpi&v fj (pcovrj bvvaTat 
ervvetpew* &(tt eXvai epavepbv otl to e^9 ovt ev tol 9 
ekay^LCTTOLS ovt ev Toh dvtcrois ovt ev {tols) lctols del 
CrjTriTeov biaciTripLacnVy dAA* dKokov\6y]Teov Tjj cpvcrei. Toz; 





I rov restituit Marquard 2 e/i/ieAels] iKfjLcXcTs H €Kfi€\€s 

iKfjLcXeTs B: eju/ieAes (/c supra priu^ fjL scr.) H *4 rifjLioXlov 

fifjLioXiov M sed post rifjLi una litt. eras., At in ras. in qua rovial fuisse 
vid; Me : rjfiirovialov V S B H 5 ^ ^ ^6 

add. Me Vb 7 ry Xixo^vov restituit Meibom 8 ficXepdcTrai 

post afjL^oripois ponit H 10 ns addidi ii Papvrcpoov nvV] 

fiapvrovfav TrapvTrdrrj Se ray ^apvr6v(av nv\ B : Papvrcpcov in marg. B 
12 xP^o’^'Toi ex x/>^®€toi Ma 14 a<popi^€(rdai H 16 koI ovx 

as ol els TO in ras. Mb 17 diB6yai H ig ov . . • tiv seelusi 

ut glossema : ov yap supra lin. add. Mb 20 ity om. eodd. praeter 

R rpiav^ Tivav B 21 (rwclpciv ex (rvyfipeiy Ma (?) oih* iy 
ex o(/T€ Mb 22 to7s restituit Marquard 23 aKoKovdeoy H 




fi€V ovv aKpL^rj \6yov rod k^rjs ovtt(o pdbtov dTrobovvat, ecoy 
hv al (TwOeaeLS r&v biaaTruMdroiiV aTioboOSicnv* on 8’ ^(ttl 
20 Ti k^rjs Kal n2 iravTeXQs diretpio (I)av€p6v ykvoir hv | 8ta 
TOLCLcrbe nvos €7rayoi)yfjs. TluOavov yap to pirjbev nvai 
bid(TTr]pLa b pLeXiobovvres els diteipa repivopiev, dAA’ elvai 5 
TLva pLeyicTTOv dpiOpiov els bv Statpetrat t&v bLaarripidTOiv 
25 eKaarov virb | rrjs pLeXtobCas. Et be tovto ^a/xez; ^rot 
mOavbv ^ Kal dvayKoXov nvaiy brjkov on ol {tov) TTpoetpri- 
pievov dpiOpLov piepri Ttepueyovres ^0oyyo6 e^rjs dWriXcav 
eyovrai. boKovcn 8’ elvau {tolovt(ov) t&v (f>66yy(ov Kal | 10 
30 ovTOL ols Tvyxdvopiev iK Ttakaiov xpdpievoi oXov r\ vrjrrf 
(Kat) ri TTapavrjTri Kal ol tovtols 

^Fixopievov 8’ dv eir] to d<l)opL(raL to ttpQtov Kal dvayKat- 
54 oTaTov T&v crvvTeiv 6 v\\T(j^v irpos Tas ipipiekets avvOeaets t&v 
biaaTTipidTOiiv. *Ez; iravTl be yevei dirb iravTos ^^dyyov 86d 15 
5 T&v e^rjs TO piekos dyopievov koX ein to ^apv Kal em ro | d^v 
Tj TOV TeTapTov T&v e^fjs bid Tecrcrdpoiiv rj tov irepLiTTOV bid 
TtevTe (Tvpicfxovov kapL^aveTco^ <S 8’ dv pirjbeTepa tovt(ov avpi- 
(iaivri, eKpiek^s eaTO) ovtos irpos diravTas ols (rvpil 3 el 3 r}Kev | 

10 dovpLcfxivio elvai Kara tovs elprjpievovs dpiOpiovs. Ov bet 20 
8’ dyvoetv, otl ovk ecTTtv avTapKes to elprjpievov Trpbs to 
epLpiek&s ovyKetirOaL rd (rvanj/xara Ik tQv btaaTripLdTCdv 
15 ovbev ydp KCdkvet o’vpi(f>(o\vovvT(ov t&v (l) 06 yy(ov Kara tovs 
elprjpievovs dptOpiovs eKpiek&s rd (rvarTj/xara avvea’Tdvaty 

3 r(p add. Mb : om. R <pav€phv^ av^pov S 5 Tifiv(aii€v H 

6 is *8 trvQavhv H tov restituit Marquard irpoeipyvxivov 
apiSjuLov Marquard : irpociprificvoi {Trpociprj in ras. Mb) apiSjuLol M V S B : 
{o*l)y€ €iprijj.€Poi apidfioX R 10 toiovtcjv restituit Marquard ii ri 
viirri Westphal : re H : rell. 12 koI add. Marquard ri 

irapav^TTj H (coni. Marquard) : ry Trapav^rrj rell. ol tovtols (Twcx^^s 

R : ^ TOVTOLS o’vvcx'^s rell. 16 tQv] Thv H 17 Thv . . . t^i'] 

H n Twv Marquard: T<p codd. 18 (rvfxtpovov S 

\a/j.Bap€Te$) conieci: \ajj.fidv€TaL codd. p/rfiiT^pov Meibom ffvfx^ 

fialvcL H 19 iKiJ.€\^s {iK in ras.) Mb : i/nficK^s in marg. B ovtus 
H ols H : iv ols rell. 20 d<Tvjj.<l>ei^poLs H $€? H : om. rell. 

22 <rvyK€7<rdaL^ KLvu<rdaL R 23 kcjKvol S (Tvix<p(i)V(i)v ivTa>v H 

24 iKjj.€\as {iK in ras.) Mb: ijj.jj.€\ 6 js R cvv^ffTavdL H: <rvvL<rTdvaL rell. 




aXXa TOVTOV /xri vitapyovTOs ovbev eri ylyverai tQv XolttQv 
o(f>€Xos. Oereov ovv tovto Trp&rov els | apyris ra^iv ov 20 
fiTj im&pyovTos avaipeirai ro fippLoapievov. "'OpiOLov 8’ earl 
TOVT(o rpoTTOV TLvh Kot (to) Ttepl TCLS tQv TeTpa)(ppb(jov TTpbs 
5 aAArjAa Oeaeus* bet yap tols tov avrov avoTrjpLaTOS | rerpa- 25 
XPpboLS iaopievois bvoLV Odrepov virdpxeLV, rj yap ovpL<l)a)veLV 
TTpbs aXXrjka, cS)(r0’ eKaarov eKaarcd avpiclxovov e^vat KaO^ 
brjTTOTe t&v avpLT^xjavi&Vy (^) TTpbs ro avrb avpicpoiiveiv /x?/ 
iTrl rbv | avrbv tottov ovvexv ovra & avpicfxovei eKarepov 30 
10 avT&v. ^Eort 8’ ov86 tovto avTapKes Trpbs ro eivat tov 
avTov avoTTipLaTOs ra TeTpaxopba^ TTpoabeiTat yap Tivcov Kal 
eTepoiiv TTepl iv tols ^Trevra / 5 ?j 1107 ]o- 6 rat, aAA’ dvev ye 55 
TOVTOV TTavTa yCyveTai ra Xolttcl dyfitjaTa. 

^FtTTel be t&v biaaTr\pLaTiK&v pLeyeO&v ra piev tQv avpicfyci- 
15 v(ov rjTOL o\(os ovK I 80K66 TOTTOV oAA’ evl pieyeOei 5 

(wpto'^at, rj TTavTeX&s aKapiaiov TLva, ra be t&v bia(l)(ov(ov 
ttoAAw TjTTOV TOVTO TTeTTOvOe Kal bta TavTas tols ahtas ttoXv 
pidXXov TOLS T&v ovpi(l)(ov(jt)v pLeyeOeat TTi\o’Tevei rj ato’Orio’LS 10 
?j rot9 T&v bLa(l)(ov(ov dKpt/360Tar?j 8’ &v eir] biacfxovov 
20 biaonfipLaTOs Xrjxfns rj bta ovpicfxovLas. ’Edz; piev ovv TTpoa- 
TaxOfj TTpbs r£ 8o06z;r6 ^^oyyo) Ka^eiv IttI ro ^apv ro | 
bidcfxovov oiov biTOVOV rj aWo tl t&v bvvaT&v \r](l) 6 rjvaL 15 
8td ovpL(j)(ovLas9 eTTL ro d^v aTrb tov boOevTos (l) 66 yyov Xrj- 

I ovd€v om. R 2 &<p€\os S 4 restituit Meibom 

TTcpl T^s] rhs TTcpl M V B S 6 dval M V B S ijroi H 

7 S>a6* ex ^6* Mx: 5 ^’ V B 8 ^ restituit Meibom fi^ om. et 

ry oifT^ Toirtp scrib. Marquard 9 ry H 13 HxpKrra H 

14 diaarrjfidreoy'B ffviJL<pe^>va}vMeibom : <rv ijl<I>($jp lav codd. 15 
oA in ras. Vb: dWcos M : dirKas Marquard doKciv in marg. B 
€vl conieci : iv codd. : ^ ci Marquard 16 &pla6ai conieci: S>pi(TTai 
codd. diatpSvav S X7-19 irdWcp . . . ^ia<piv(av om. R 19 rols 
ex ras vel rais in ras. Mb 3 * del. Marquard 20 fi in ras. Mb 

22 3iTovov~\ 81 in ras. Mb. fuisse vid. n vel re: oTov re rovov in marg. 

B 23 iiri de rh punctis post enl V: 8e scripsisse vid. Mb, eras. 

Me y^?) ; iiri 8e rh S, B (sed punctis in marg. additis) 






irreov to 8ta Tecrcrdpoiiv, etr em to fiapv to bta TrivTe^ €?ra 
20 t:6Xiv em ro | o^i; to bia T^aadpcov, etr’ em to fiaph ro 
bta 7r€VT€. Kal ovto) 9 iaTat to biTOVov dito tov krjcpdevTOS 
(l)66yyov elkripipLevov to iirl ro ^apv. lav 8 ’ lin tovvovtiov 
25 TTpooraxOfi AajSeti; ro bid(f>(o\vov^ evavTicos 'noirpriov ttiv t&v 5 
crvpL(l)(ov(ov \fj\lrLv. TtyveTat be Kal edv dirb o‘vpL(j)(ovov 
biaaTTipiaTOS ro bidcfxovov bid (TvpL(l>(^vias Kal ro 

30 Xoimv bid (rvpL(l>(^vias eldrjpipLevov dcfyaLpeiaOcd | ydp ro 
biTOVOv dird tov bud Teacrdpotiv (8td) (rvpLcfxovias* brjXov brj 
OTL ol Trjv iirepox^v ireptexopTes y ro bid Teaadpo^v vTiepexei 10 
TOV biTOVOv bid crvpLcfxovLas eaovTai irpds dXXriXovs elXrjpi- 
56 pievor v7rdp\\xov(TL piev ydp ol tov bid Teo-adpcov opoi avp.- 
(fxovor dird be tov o^vTepov avTciv Xapi/SdveTai (pOoyyos 
(rvpL(l)(ovos eirl ro o^v bid Teaadpotiv, dird be tov \i]\(l)0evTos 
5 eTepos eiri to papv oia irePTe^ \eiTa iraAiv eiri to o^v oia 15 
Teo-adpcoVy) etr’ otto rovrov eTepos eirl ro / 3 apv 8td irevTe. 

Kal ireiTTcoKe ro TeXevTaiov oijpLcfxovov eirl tov o^Tepov t&v 
10 (jyv) vTiepoyriv opi^ovTcov, &(tt eivai (I)a\vep6vy ort, edv dird 
(TvpKfxovov bid(l)(ovov d(l)aipe6f} bid (rvpKfxovias, eaTai koli 
ro Koimv bid (Tvpi(f>(ji>vias elkrjpipLevov. 20 

Oorepoz; 8’ opO&s viroKeiTai ro bid Teo-adpotiv ev dpxy 
15 bvo Tovcov Kal ripii\(Teos, Kara Tovbe Tdv Tpoirov e^eTdaeiev 
dv T19 dKpi^ecTTaTa* el\ri(f> 6 (o ydp ro 8td Teo-adpotiv Kal irpds 
eKaTepcd t&v opcov dcf^opiaOco biTovov bid ovfjicfxovias. brjXov 
20 oTi dvayKaiov rdy | virepo^ds icras eivai, eTreibrjirep Kal 25 

I elra cKre H 2 €t iirl B : eJr* iirl in marg. B : €^ r* iirl S 
StaTreVrel supra lin. add. Mb 4 <pd 6 Yyos MVS del. Meibom 

7 ante a<l>aip€d^ una litt. eras. M : at in ras. Me: € in ras. Mb 

8 a<l> 7 ip€i(T 6 (t) MVS: acprip^icda) B R 9 tou] rrjs H $t^ restituit 

Marquard ii diT 6 vov\ post t litt. a eras. M : diarSpov B 12 y^p 
om. B 5 pot] 01 in ras. Mb: opdol R, B in marg. 15 elra . . . 

T€(T(Tip(av restituit Meibom 17 rhv Meibom: codd. 18 r^v 

restituit Meibom 19 avfKpd^vovs H did<pa}vov~\ dia in ras. Mb 

24 dirovov Meibom : (TvfKpeovov codd. 




taa aiT t<T<ov a(l)fifyqTaL. juiera 86 tovto t& to o^repov 8t- 
Tovov 6776 TO jSapv opt^ovTL dtct Tecradpiov €l\rj(l)6o) Itti ro 
d^v, r£ 86 TO Papvrepov birovov iirl to | o^v opt^ovTL 25 
€l\'q(l)6(o €T€pov bid T€(r(rdp<t)v eirl to fiapv. (fyavepov 8r} 

5 OTL TTpos eKaTepcd T&v opL^dvTcov TO ytEyovbs (TuoTrjpLa bvo 
(Tvvex^'f^^ 6(roz;ra6 Ketpievat virepoxcu hs avayKoiov | taas 30 
€LvaL bta ra epiirpoaOev eiprjpieva. TovT(av 8’ ovtcd irpoKOTe- 
aKevaapievcov tovs aKpovs^ tQv d>pL(TpL€V(ov (l)66yy(ov iirl t^v 
al(T6r](Tiv €TravaKT€Ov ei pi^ev ovv (fyav'qo’ovTat bid(l)(ovoLy 
10 brjXov OTL ovK €(TTaL TO bia T€(T(rdp(ov bvo ro| \v(ov Kal fipLUireos, 57 
66 86 (Tvpi(\>oiivri(Tov(n bid irevTe [Teacrapa,] brjXov otl bvo 
t6v(ov Kal fipiiireos eaTat to bid Teacrdpcov. 6 piev ydp 
^apvTOTos T&v €i\ripLpL€V(ov I (l)66yy(ov bid Teiradpcov ‘qppLOO’drj 5 
(Tvpicfxovov T (0 TO ^apVTepOV blTOVOV ^776 TO O^V Opi^OVTL, 

15 Tov 8* O^VTOTOV T&v €l\ripLpL€V(ov (f>6dyy(ov bid irevTe avpi- 

(TvpL^(t)V€LV r5 ^apvTdTiOy SaTe | virepoxv^ ic 

ovaris Toviaias r6 Kal els icra birjpripiivrjs &v kKaTepov fipuTo- 
VLov T€ Kal virepo^^ T€(r(rdp(ov icTTlv virep to 

biTOVoVy brjXov otl irevTe fipLiTovioiv avpi^aiv^i to bid Tea- 
20 adpodv I eivai. "'Oti 8’ 01 tov Kr]<l> 0 ivTos (rvaTrjpiaTos aKpoi 15 
ov (rvpL(^(jCivri(rov(nv aXXriv ovpiclxoviav ^ t^v bid TrevTe, pabiov 
ovvibeiv TTp&TOv pi€V ovv oTi Tr]v bid Teacrdpcov ov (rupi- 
<l)(ovov(ri KaTavor]T€ov, | 677668?j776p irpos r5 Xr](f> 6 €VTi 20 
CLpXV^ 86a T€(r(rdp(jt)v virepoxv irpoaKeiTai 6^’ kKaTepa* 677660’ 

25 076 TTjv bid iraaoiv ovk evbex'^Tai (rvpi(l)(oviav beiKTeov. to 

3 PapvT€pov\ rh om. R fiapurcpov Va R : ^apvrovov M Vb S B 
Sidroyoy R 4 €T€poy H ; tripos rell. 6 Kelficyai conieci: /cal /j.^ 

%v at codd. : /cal /j.^ fiia at Marquard 7 TrpoKara<rK€va<rfi 4 y(i>y B : 

vpoffKarcffKeuaffixivcav H 8 dpi^dyray M (sed (dyr in ras. Me) R H : 
dpKr/xay &pi<rjj.€y($jy Yh rell. 10 dridrjXoySri 1 ^ 11 <rvjj.<pe$)^ 

ydlffaxTi M Tcaffapa del. Marquard 15 5 *] T€<r<rapa M V S B : 

rdrapToy R 16 (rvipcoycTy S 17 dirjpruJLcyris ex diripri/uLcyriy 

Me: diripriiJ.€yriy Y 1 ^ S 18 seelusit Marquard 19 

ToviaioDV H T€a<rdpeoy Meibom : ircyrc eodd* 20 ot] fj S 

25 deiKTcoy Marquard : \^kt 4 ov eodd. 

L 2 



yap €K T&v VTT^poy&v ytyvopievov /x^yeBos ekarrov ecrri 
25 biTovov, eXdrrovL | yap vTrepex^t to bta Teo’o’dpoiv rj t6v<o 
T ov biTovov* ovyycopeiTai {ydp) irapa irdvrayv to bua rea- 
(rdpcdv pl€lCov pL€V eivat bvo T6v(t>v eXaTTOv be rptcSz;, cSore | 

30 TTCiV TO 'npoo’Keifxevov t& bid Teaadpcov ekaTTOv eaTi tov bid 5 
7 revT€* (f>av€pov {brj) otl to ovyKeipievov avT&v ovk dv 
€ 17 ] bid iracrciv. el be (rvpLcfxovovo'iv ol aKpoi t&v k 7 ](l) 6 evT(ov 
58 (f)96yy(i)v /xet^o) piev || ovpLcfxaviav Trjs bid Tea’(Tdp(i)V ekdTTto 
be Trjs bid Traa&v^ dvayKaiov avTovs bid irevTe oijpicfxoveiv 
TOVTO ydp eaTi fiovov pieyeBos aijpLcIxovov /xera^ tov bid | 10 
5 Teairdpcav Kai tov bid iraaoiv. 

2 dirSvov] post i una litt. eras. M cXdrrovi] tXarrov R xnripx^t H 
3 diroj/ov ex dirrdj/ov M c : dirrdi/ov S dwd ante 

Marquard ydp addidi 5 ry] M V B S 6 5 )) restituit 

Marquard : 56 H : om. rell. 10 tovtov H <r^p<pcuyov'] inter v 

et o una litt. et in eo acc. eras. M t€ post ficra^v tov add. H 



2TOIXEiaN r' 


Ta k^s T€Tpd)(ppba rj (n;z;|rj7rrat rj KaX€L(r0(o 15 

86 (Tvva(l>^ [i€v OTav bvo T€Tpaxppboi)V 1^9 pL€\(oboVpL€VOi)V 
SfiOLcov Kara o^iia (^0oyyo9 rj dva pLeaov kolvos, btaC^v^iS | 

8’ OTav bvo T€Tpaxopb(ov k^s [xeXcdbovpievcov opLoicav Kara 20 
5 o^rjfia Tovos fj dva pieaov. "'Otl 8’ dvayKaiov erepov irorepov 
(rv[jL^aiv€Lv ro49 k^s TerpaxppboLS, (l>av€pov €K t&v vtiok^i- 
pi€V(ji)V I ol [i€v yap Teraproi r&v bia T^crcrdpoav (tv/x^o)- 25 
vovvTes (rvva(l>^v TTOiTjcroviTiv, ot 86 || Tre/xTirot 84a irevre 59 
bid^ev^LV. beu 8* erepov irorepov tovt(ov virapyeiv tols 
I ^0oyyo69, axrre ical rois k^ijs rerpay^opboLs dvayKaHov erepov 
T&v €lpripi€V(ov V 7 rdp\X€iv. 5 

^H8i7 be Ti 9 'qiToprja’e t&v aKovovrcov irepl rod 6^9* TTp&rov 
fiev Ka 06 \ov t( ttot earl to 6^9, e^retra noTepov Kara eva 
pLOVov yLyverai Tpoirov rj KaTa irketovs, Tpi\Tov 8’ el 40*0)9 10 
15 ajLi^oV6/)a raSr* eaTlv e^s Td re ovirqpLpieva Kal tcl 846- 
C^vyfieva. Ilpos bi] Tavra tolovtol TLves ekeyovTO Xoyoi* 
Ka 06 Xov Tama eXvai crvcTTripxiTa ovveyfj &v ol Spot ijtoi e^s 

2-4 orap ... orap 5 iJol erat 5 t€, t* Up supra lin. add., re corr. in dvo, 
et T€ inscr., reliqua in marg. Me : om. V B, R (sed ‘postea alieno loco 
interponuntur ’ v. Herwerden) * 2-5 5 t€ pro Urap 8 vo leg., i^rjs 

• . • (Tyriixa om. S 5 t 6 t€Pop om. H 7 rdraproi B; 5 rell, 

<rvix<p<&p(i)p 6 pt€S H 9 8 €i Meibom : r( codd. 12 rd 8 e post 

efijs add. H 14 fiopop Me (supra lin.), R H : opop MBS rpdvop^ 
rpdir e corr. V Kara om. H 8 * cl Marquard : 8 c codd. 

16 5 ^ H : 8c rell. TOiovTOP B 17 <rva’'rfi/iaTa ex cv<rri\ixa 



III. 59 


15 €l(rlv rj I € 7 raXXdTTov(Tiv. tov 5 ’ bvo rpoirot dcriy kclL 
6 [JL€V {KaO^ ov T& TOV o^ripov crvcTTruxaTOS ^apvrepia opio 
KOIVOS IcTTlV 6 TOV ^apVT^pOV (TViTTrjpiaTOS opos) O^VTepOSy 6 
8’ €T€pos KaO^ bv 6 tov o^vripov (rvarripLaTos ^apvTepos opos 
k$rjs €(rTl rfi TOV fiapvTepov (TVOTrjpiaTos o^vripcd op(o. Kara 5 
20 piev ovv TOV I irpoTepov t&v Tpoircov tottov re tlvos kolv(ov€l 
ra tUv T^Tpayopboiv (rvcrrrjftara koX opLOta eartz; e^ 

dvdyKTiSy Kara 8e tov eTepov Keyj^purTaL dir dXXrjXoiv Kal 
25 opLOia bvvaTai yL\yv€(T 6 ai ra eXbrj tS^v T€Tpaxppb(ov* tovto 8e 
yiyveTdi tqvov dva pLeaov re0ez;ro9, dXXais 8’ ov. coare bvo 10 
Terpdyopba ojutota Toiavra avpi^aiveiv k^rjs dXXrjXcov etvai 
30 &v 7/ro6 Tovos dvd | piecrov eorlv rj ol opoi eiraXXdTTOViriv. 
wore ra e^9 TeTpdyppba opLOia ovtq, rj (rvvripipieva dvayKOiov 
€LvaL rj bteC^vypLeva. 4>a/xez; 8e 8etz; tQv k^rjs rerpa^opScoz; 

60 7/rot airX&s Pfrjbev et||z;at dva p^icrov Terpdyppbov rj pLrj 15 
dvopoiov. T&v pL€V ovv OpOiCOV KOT etboS T€Tpaxdpb(OV ov 
TiOeTat dvopoLov dvd piaov Terpdypf^oVy t&v 8’ dvopoLCov 
5 pev I k^rjs 8’ ov8ez; TiOeaQaL bvvaTov dvd picrov Terpdyppbov. 
’Ek 8e rcSz; elprjpivcjav (pavepdv otl ra opoia kot etbos 
T€Tpdxopba Kara 8vo Tpoirovs tovs elprjpevovs k^rjs dXXrjXoiv 20 
TeOrjaeTaL. | 

10 ^AovvOeTov 8’ eart bifdorrjpa to vtto t&v (f^Ooyycov 
Treptexop^vov. el ydp e^rjs ol TreptexpVTeSy ovbels eKXip'ndveiy 
pri eKXipirdvcov 8’ ovk e/xTreaetrat, p^ epm 7 rr(t)v 8’ ov 8tat- 
15 prjaeiy o be prj biaipecriv e)(et ov8e avvOeatv | e^er ttclv ydp 25 

I €l<r\v in ras. Ma : om. V B S iva\\dTTOv<riv ex €Tr€\aTTov<riv Mb 
(ut vid.) 2 KaS’.. . Spos restituit Meibom 3 o^vr^pov B 

4 o^vT€pov om. B 6 rpdirav Marquard: 6 pS>v B : ^pcjv rell. 

Koiv(avov(nv H 7 Hfioid Meibom: avdfxoia codd. iffrip om. H 

II ante ^juLoia 2 litt. eras. M roiavra Marquard: ravra codd. 

(rvfifialv€i B 13 jjrot H ^5 ^ V-h Meibom : ci e/ /a)) B: 

€i rell. 16 dvdfioiov Meibom : tfioiov codd. 17 rlOeffdai H 

av 6 fioiov Meibom : ^/uloiop codd. 17 tcjv 5 * . . • rcrpdxop^oi/ 

om. R 18 rld^ffBai ex rlderai Me : rlderai rell. 19 Se] 5 )) H 
22 Biao’T'fifiara R 25 dialpcaiv ex dialprjffip vel vice versa M 

e'let] B 



III. 6o 

TO (TvvOerov Ik tiv(^v ixep&v iorl (ruvOerov els airep Kal 
hiaiperov. Viyverai be koI ire pi tovto to 7rpo/3\?j/xa TrXdvrj 
biCi TTjv T&v pieyeO&v KOLVorqTa rotabe tls* OavpA^ovcn yap [ 
770)9 TTOTe TO biTovov dovvOeTov 0 y eoTL bvvaTov bieXe'iv els 20 
5 Tovovs ^ 770)9 'Kokiv TTOT eorlv 6 TOVOS CLovvOeTos bv y eaTl 
bvvaTov els bvo rjpLiTovia^ieKeiv* tov avTov be koyov Keyovcri 
Kcd I 776pt TOV fipLLTovLOv. TLyveTai 8’ avTois Tj dyvoia irapa 25 
TO piTj (Tvvopdv OTL T&v bia(rT7]pLaTiKG>v pieyeO&v evia Koiva 
Tvyyavei ovTa ovvOeTov Te koX davvOeTov bLaorrjpiaTos* bta 
10 yap TavTTjv TTjv | axTiav ov pieyeOei biaarrjpiaTOS to daiJvOeTOv 3® 
dXXd 7069 TTepieyovcn (pdoyyoLS dcfxopLorau to yap biTovov 
oTav piev opi^odai pLearj ml kixcf^vos, dcrvvOeTOV eaTiVy OTav 
be pLeoT] ml TrapvTraTr], oiJV\\6eTov bu OTtep (l)apiev ovk ev 61 
7069 pLeyeOeat t&v biaoTripLaTcov eXvai to dcrvvOeTov ev 
15 7069 'nepieyovcn (pOoyyois. | 

^Ev be Tats t&v yev&v bLa(l)opa'LS Ta tov bid Te<r(rdp(ov piepr] 5 
pLOva KiveiTaiy [70 8’ 6860z; 7rj9 btaCev^ecos dKivrjTov 60T6z;.] 
TTCLV piev yap btriprjTo to fippLoapievov els orvva(l)i]v Te ml 
bid^ev^iVy 0 ye ovveaTrjKev | Ik 'nKeiovcjav ^ 6z;o9 TeTpa^opbov. 10 
20 ’AAA’ Tj piev (rvva(f>ri Ik (j’&v tov bto) Teacrdpcov piep&v 
piovcov [dovvOeTOiiv] eroyKeiTaiy &(tt e^ dvdyKris ev ye TavTrj 
Ta TOV bid Tecrcrdpcov piova piepr) Kivr\Qrj(TeTai* fj be bidC^v^is | 
686 oz ; 6)(€6 irapd Tavra tov tovov. edv ovv bet^Oy to ibiov 15 

I post KoX ras. M 2 adiatpcrov VS dh Marquard : dij codd. 

4 7r«7roT€ H affvvdcT ov Ma, sed ov supra Bcr et acc. et spir. add. 
Me 5 y conieci: om. V S B : "bv rell. 5 ir&s post irdXiv 

ponit H ird\iv^ iv ras. in Me : irdKai VS 6 icrlv post Bvvarbv . 
ponit H db Marquard : 5 )) S : Bh 5 )) relL 12 bpi^ovai B 

13 post ffifvBcrov in une. quad. dAA* iv roiis Tr€pi€xov<ri <pB6yyois S 
IT rh d* , . . iffriv seelusi 19 dieit Marquard ‘ post t una lift, 

eras, quae v fuisse vid. M *: sed ego quidem yc fuisse suspieor. 
Quod si legitur, turn eerte verborum translatione nulla opus est: 
neque, si omittitur, ordinem librorum mutare velim verba t . . . 
TCTpax^p^ou post Tjpfioa'iuLivov ponit Meibom 20 tcjv tov Bid addidit 
*Westphal 21 fx6vov H davvBirav seelusi 23 

Meibom : €Xoi eodd. napd ravra^ irapd post ravra eras, et supra 
lin. add. Me ravra wapd V B S supra lin. add. Mb (?) 

III. 6i 


Trjs kivov\i^vov ev tols t&v yevQv bLa(l)opaLSf 

brjXov 076 AeiTTerat ev avrots tols tov bta Teacrdpoiiv pLepecri 
20 T^v KLvrjaLV etvau ^Eort 8’ 6 | piev ^apvrepos tS>v {tov) 
Tovov 7 repi€XpVT 0 i)v o^vrepos t&v to rerpdyppbov 7 r€pi€)( 6 vTO)v 
TO ^apvTepov tQv ev Trj Sta^ev^et K€ipL€V(ov* [ 6 pLo((os 8’] 5 

(8’)[ Kal] ovTOS aKivriTOS kv rat? TOiv^yevS^v bLa(l)opaLS* 6 8’ | 

2.5 d^vTepos T&v ijov) TOVOV 7r€pi€x6vT(ov ^apvTepos t&v to 
T^Tpayopbov 7r€pi€x6vT(ov to o^vTepov tQv kv Trj btaCev^ei 

30 bia(f>opaLS. "'Qlo’t kiretbr} | (pavepbv otl ol tov tovov Trepte- lo 
yovTes CLKivriTOL eiatv kv Tats tS^v yev&v bLa(l)opaLS, 8^ Aoz ; otl 
keiiTOLT &v avTCL TO, TOV biCL T€(r(rdp(ov pikpri piova KivecirOaL 
kv 7069 elprjpikvaLS biacpopais. 11 

62 ’Ez; eKaoTO ) be ykvei TOiravra kcTTiv davvOeTa ( 7a ) irketiTTa 
bcra kv t& bed irevTe. Daz; piev yap ykvos jjtol kv (Tvva(l)fj 15 
5 pLeXiobeiTaL rj kv biaCev^ety KaOdirep | epurpoaOev etprjTat. 
bebeLKTat 8’ fj piev (rvvacl)^ kK t&v tov bud Teiradpeov piep&v 
pLovcov (rvyK€ipL€vriy rj be bidCev^iS kv Trpoo’TiOe'iO’a to tbiov 
10 bidaTTipLa, tovto 8’ korlv 6 tovos* irpoaTeOevros 86 | 70S 
TOVOV irpos 70 70S 860 Teo-adpoiiv piepr] to bid rrevTe ov / x - 20 
TrkqpovraL. "'Qlo’t elvat (l)avepbv 076 , kireibrjirep ovbev t&v 
yev&v kvbeyeTai ko 7 o pitav yjpoav kapL^avopLevov kK Trkeiovcov 
15 d(rvv 6 eT(ov (rvvTe\ 6 rjvai t&v kv t& bid nevTe ovrcjavy [8rjAoz; 

2 TOis om. V B S 3 rhv restituit Marquard 4 r 6 v(i)v 

B R 5 TTcpi^xivTtav post fiapvTcpop ponit H Sfioleos 8* et Kal 

seclusit, et 8’ addidit Westphal 7 rhp restituit Marquard 

fiapvT€pos • . . TTcpicx^vTcov ill marg. Me; om. VB : r6vov irepiexkvTCJv 
rh rh fiapvrepov o^^repov rS>v iv 8. S 8 Trcpiixovr<av 

post rh o^vT^pov ponit H o^vrepov ex fiapvrcpov Mb : ^ojpin^pov B 
10-13 . . . clprj/jLcvais dia<l>opa7s om. R 10 Sri supra lin. add. 

Me; om. VB S 12 XcIttoit^ cXttoit R Kivclrai B 14 to 
addidi 16 ipLirpoffd^v om., et Trp 6 T€pov post cXprjrai add. H 

18 ix 6 v<av Meibom : ix 6 vr) eodd. %v irpoffridc^ffa eonieei; ifiirpoffBcv 
rcBclffa eodd.; npoffriBcla’a Marquard 22 Kafxfiavoixcv B in 

marg. 23 iv ra ex €/c rav M : e/c rav V S B BrjXop %ti seelusit 


APM0Nlki2N STOIXEIilN / III .62 

on] kv eKaana yevet To<TavTa lorai ra TrAeiora a(r 6 vBera ocra 
kv rfi hia irkvre. 

Taparreiv 8’ etoiiOev kviovs kclI ev rovrw r£ irpopXrjiJLaTL 
TTcis TCL TrAetora | TTpooriOeraL koI bta tl o^x clttX&s becKwrat^ 20 

Saa eoTiv kv r£ 8ta irevre. Upbs oiis ravra Aeyerat, on 
k^ kXarrovcdv aovvOkrodv lorat ttoO^ €Ka\(TT0V t&v yev&v 25 
avyK€Lpi€Vov 6K Tr\€i 6 v(ov 8’ oibkirore. Ata ravTrjv be r^v 
alrtav tovto avrb Trp&rov airobeiKiwrai, on ovk kvbkx^TaL 6K 
10 TrkeLOvcov aavvOeTcov (TVvreOfjvaL t&v ye\v5iv eKaarov rj oaa kv 3^ 
r£ 86a irevre Tvyydvei ovra. on be Kal e^ ekarrovcov irore 
awTeOrjaeTai eKaarov avr&Vy kv tols eTreura beiKwrai. 

YIvkvov be irpbs ttvkvQ ov /x6Aw866||ra6 ov 6 ^ okov ovre 63 
pApos avTov. ^ypL^rjaerai yap /xTjre tovs rerdprovs r£ 86a 
15 Te(r(rdp(jt)v ovpLcfxjDveiv /xTjre tovs TrepLirrovs r£ 86a irevre* ol 
be ovT(o Ketfievoi | tQv (l) 66 yy(ov eKpiekets ^aav. t&v be to 5 
biTovov irepLexovTCov 6 piev ^apvrepos o^vraros eon ttvkvov 
6 8’ o^vrepos ^apvraTOS* dvayKOLOv yap kv Trj (rvva(l)fj r&v 
TTVKv&v bid reo’o’dpcov (rupL\(f>(ovovvT(ov dvd pikaov avr&v 10 
20 K66(r0a6 ro birovov, dxravrcds be Kal t&v btrovcdv bid 
Te(r(rdpa)v orvpLcfxovovvTOtiv dvayKatov kv pietTip KeuirOaL to 

I (Tvvdera R 8<ro iv ry om. R 3 €^el) 6 €v] v postea add. M 

4 TTws in marg. Mb 5 (TuyK€iiJ.€v 6 v iariv ante cKaffrov add., et 
(Tvvi<rrr)K€v om. H 7 ecrrat 7ro0’ om. R : etrrat iroQ* %Ka<rTov om. V 

ecrrl post ycvav add. R,Mc (supra lin.) post ycvav add. (rvvcffrr^Khs 
oca iffrlp iv ry 5 to irevrc, irphs ots Xcycrai ^ri €( iAarrcSyofy affvpdcreop 
tS>v ycvav S B Vb in marg., nisi quod <rvv€<rTriK 6 s om. Vb, rap ycvav 
om. Vb, rav om. S 10 ^ eras. M : om. V S B H 14 rerdprovs 
Marquard : 5’ in marg. Me, S : om. Va : ria’ffapas rell. ry] H : 
post Tco litt. p eras. M : rap VB 15 ttcplittovs Marquard ; ircpre 

codd. ry add. Me : om. V S 01 Se l oifd* H 16- post 

oUtoj litt. <T eras. M e/c/xeAels ex ifipicKcTs Me; i/mfieXeTs V B S 
17 fiapvrepos Marquard : ^apvraros eodd. o^vraros • • . fiapvraros 
oin. R 18 fiapvTcpos B, sed in marg. fiapvraros 20 K€ 7 <rdai 

om., et cJpai post diropop add. H t^] rhp VS §€ om. S post 
Kal add. ip (rvpa<p^ in marg. Me, ttJ <rvpa<py R rb ante did r€(r(rdpafp 
add. H 21 post litt. p eras. M : rbp V S B 


III. 63 


15 TTVKvov TovTCdv 8’ ovTO )9 lyovTCjdv avayKalov I ivaXXa^ TO re 
TTVKvov Kal ro biTovov K€i(r 0 aLy wore brjXov on 6 [jLev ^afrv- 
repos T&v TrepLexpvTcov to birovov o^raros ecrrai tov eiii ro 
20 ^apv Keipievov ttvkvoVj 6 8’ o^vrepos tov em to o^v \ Ketpievov 
TTVKVOV ^apvTaros* ol be tov tovov Trepieyovres apL(f> 6 TepoL 5 
elcTL TTVKVOV ^apvTaTOiy TiOerai yap 6 tovos ev rfj btaC^v^ei 
pLera^v tolovtcov Terpayopbiov h ol TrepLeyovres l^apvTaToi 
25 el(Ti I TTVKVOV* VTTO TovTOiv be Kcu 6 Tovos TTepLeyeTau 6 piev 
yap jSapvTepos t&v {tov) tovov TrepLeyovTcov o^vrepos ean t&v 
TO ^apvTepov t&v Terpayopbcov Trepieyovrcjavy 6 be o^repos lo 
30 T&v {tov) tovov TrepLeyovTcov Pa\pvTep 6 s icn t&v to o^vrepov 
T&v rerpayopboiv TrepLeyovTOiVy axrr eXvai brjXov on ol tov 
TOVOV TTepLeyovres jSapvrarot ecovTai ttvkvov. 

64 Avo be biTOva e^rjs ov TeOrjcreTaL. Ti6e\\(r6(o ydp* clko- 
kovOrjaeL brj rS piev o^repia btrovio ttvkvov Itti to fiapvy 15 
o^raros yap ^v ttvkvov 6 eTrl to ^apv opi^o^v to birovov* 

5 r£ be jSapvrepio bL\T6v<o eTrl to o^v aKoXovOrjaei ttvkvov, 
^apvraros yap rjv ttvkvov 6 eTrl to o^v 6pi^(ov to birovov. 
Tovtov be avpifiaivovTos bvo ttvkvcl e^rjs TeO'qo’eraL* tovtov 
10 be eKpiekovs ovtos eKpiekes earai | Kal ra bvo birova e^rjs 20 

’Ez; appLOvia be Kal ypoipian bvo roviaia e^rjs ov re^Tjo-erat. 
TiOeaQo) yap eTrl to o^v Trp&rov* dvayKaXov 8 ^ ehep earlv 

I ei'oAAof] acc. add. et postea 2 litt. eras. Me : ei'oAAafot V B S (sed 
ivaWa^ in marg. B) 2 ^ap^Lnepos Marquard : fiapvraros codd. 

4 TOV 67 ri o^h K€i/jL€vou iwKvov in marg. Me: om. V S B 5 ttvkvov 

oin. R Pap^naros Marquard: PapTLfTcpos eodd. ot] 6 B 

7 TOiovTov B Ma, sed &v supraser. Me : cov R Trepicxovres 

ex TT€pi<rxivT€s Me 9 Papin epos Marquard: Papinaros eodd. 

rhv restituit Marquard t 6 v(ov R Trepiex^VTCJV om. R 10 rh 
supra lin. add. B : om. S Papvrepov Marquard : Papitrarov eodd. 

rav rerpaxop^Tov^ rwv supra lin. add. Mx : om. VS ii rhv 

restituit Marquard (legit H) 12 rav t6t.] tcov supra lin. add. 

Mx ; om. Va S 14 dlrova'] post i litt. a eras. M : didrova V B S 

18 diopl^oDV R 20 eK/j.€\€<r 6 ai supra e aee. eras., r supraser. et 

in marg. e/c/ieAes effrai add. Me: e/c/xeAes etrrot (es ear e eorr.) Vb 
Kal om. H didrova MVS 22 ivapfidvia S 23 5 ))] Se V S B 


III. 64 


6 roz; irpocrTeOevTa tovov [ opt^cov <^ 0 oyyo 9 Im ro 15 
o^v (rvpL(f>oi>V€iv rjroL rfi rerdpria t&v k^s bta recrirdpcov rj 
T& Tre/XTrrw bia 'nivrv /xrjSerepov (Se) tovtohv avT& crup,- 
fSatvovTos dvayKaZov czc/xeA^ ^tvai. otl 8’ ov (rvp\Pri(r€Tat 20 
5 (I)av€p6v Ivappovios pev yap ovaa rj ki^avos r^aarapas 
Tovovs diTO Tov Trpo(r\r](f> 0 €VTOS (f> 06 yyos Terapros &V9 

Xpo^paTLKTi 8’ €LT€ paXaKOv xp(6paTos 660’ ripioKiov piei\Cov 25 
d(l) 4 ^€L btdoTripa rod bta 7r6z;r6, roviaiov b\ yevop^in] bta 
7 T€VT€ (Tvpcfxovricrei T& 7rpo(r\ri(l>0€VTL (f) 06 yy<o. ovk ebei b 4 
10 ye, dXXa rjroL rbv rdraprov bta T€<7(rdp(ov (rvpifxovelv ^ rov 
TrepiTTov biJd 7rev\T€. Tovt(ov 8’ ovb^r^pov yiyverai, wore 3® 
(I)av€p6v, OTL eKpeXris eorat 6 rbv Tr/xxrArj^^eWa rovov opC^oiv 
^0dyyo9 6776 TO 6^. ’EttI 86 ro fiapv TL 0 ip^vov to bevr^pov 
TOVLaZov bidrovov 7 ro 6 ?j(r 66 ro || y 4 vos, coo-re br}\ov otl ev 65 
15 dppovia Kal xpcapan ov r 6077 O' 6 ra 6 bvo rovLaZa k^s. ’Ez; 
bLarovif 86 rpia TOVLaZa k^s T€ 07 i(r€TaL, TrAecco 8 ’ ov* 6 yap 
TO rkrapTrov | tovloSjov 6pL^(ov (f)06yyos ovre rS rercxprco bta 5 
T€cr(rdp(ov ovt€ rfi Tre/xTrrco 86a Trez^re crvp(f)(ovrj(r€L. 

’Ez; r£ avr£ 86 y6z;66 rovrco 8vo fjpLTovLaZa ov re- 

20 0 rj(r€TaL. T 606 o- 0 co yap | Trpfiroz; 6776 ro jSapi; roS virapyov- 10 

r09 fjpLTOVLOV TO 7rpO(rT€0eV rfpLTOVLOV* (TUpfiaLVeL bj] TOV 

opt^ovra (f>06yyov ro 7TpooT€0€V ^pltovlov prjT^ rfi rercxprw 
86a T€(r(rdp(ov avpipcoveZv prjTe r£ 7rkp\7n‘<o 86a irevr^. ovtoo 15 

I ex €Kjj.€\^s Me: €Kjj.€\^s V S, B (sed in marg. ifificK^s) 

3 T&v ante $ia ttcvtc add. R /nrj^ krcpcD tovto ex jj.rid* krSpoo tovtoj 
M : fiTj^ €T€pcp To{fT(p V S B 56 restituit Marquard avr&v ex 
avT$ Me avT^ post (rvixfiaivovros ponit H 6 B (sed 

a<p€^€i in marg.) 10 aAA* rjroi ex dAAa rot deinde 2 litt. eras. Me : 
oAA^ ToiovTO V B S : dAAa rhv in marg. B Teraproy] 5* S ii 56 
in marg. Me : om. V B S 13 ivl rh ofv iirl rh o(v (cum punetis 

sub iwl rb o(b altero) B devrepov roviouov Ma, sed jB supra bevrepov 
et a supra roviouov add. Me 17 t 5 om. H 19 f)puToviouoi\ 

Tovioua V S B et Ma, sed tj/uli supra lin. add. Me riOerai in marg. 

B, R 21 TijuLiToviaiov B 5^ H: 56 rell. 22 rb 

supra lin. add. Me : om. V B S 23 avjuujxovoTv post 5td ircvre 

ponit H 


III. 65 


fi€V ovv €OTat tov TiiiiToviaLOV fj Oiais. iav 8’ eiri 

TO d^v T€0fj TOV VTTapxovTos, xpS^ia iaTaiy wore brjXov otl 
€V biaTOvia bvo ^pLiTOViOLa ov T€0'q(r€TaL 1 ^ 9 .—Oota [lev | 

20 ovv tG>v a(rvv0€T(ov bvvaTai Lira k^ijs T[0€(r0ai Kal Troca tov 
api0ix6v Kal TTOia TovvavTiov '7r€TTov0€V ttTrAfi? ov bvvdpieva 5 
TL0€(r0ai taa ovTa 6^9, bebeiKTar Trepl be t&v dvCo-onv vvv 
XeKTeov. I 

25 HvKVov p.ev ovv 77/009 buTovia Kal €776 TO ^apv Kal eirl to 
d^v TL0eTaL. AebeiKTaL yap ev Trj avva(l)fj evakka^ T(,0epLeva 
Tavra ra StaoT^/utara, <5 ot€ brjkov otl eKorepov eKaTepov 10 

30 Kal €776 TO ^apv Kal I €776 TO o^v Te 0 rf(TeTau 

Toz ;09 §€ 77p09 blTOVid €776 TO O^V piOVOV TL0eTaU T6- 

0e(r0<a yap eirl to jSapv* (TvpL^'qo’eTai b^ irCiTTeiv eirl t^v 
66 avT^v Taaiv 6^vTa\\T6v Te ttvkvov Kal /Sapvraroz;, o piev yap 

TO blTOVOV €776 TO /3apV Opi^COV O^VTOTOS ^V TTVKVOVy 6 §€ TOV I5 
5 TOVOV €776 TO O^V ^apVTOTOS. TOVTOiiV be irnTTOVTOiV I €776 
TTjv avT^v TacTiv dvayKaiov bvo irvKva TC0e(T0aL. tovtov 8’ 
eKpiekovs ovTos dvayKaiov Kal tovov eirl to ^apv biToviaiov 
eKpLekrj eivai. 

lO Toz ;09 8€ 77 p 09 7 rVKV& €776 TO fiapv | pLOVOV TL0eTaL. Tl- 20 
0ea0a> yap em TovvavTiov* (TvyL^ricreTai bri ro avTo irdkiv 
dbvvaToVy €776 yctp T^v avTTjv T&aiv o^raro9 Te ttvkvov 
T reaeLTai Kal ^apvTaTOSy dxrTe bvo TTVKvd TL0ea0aL 1^9. 

15 TOV I TOO 8’ ovTos eKpiekovs dvayKaiov Kal TXjV tovov decnv 
T^v eirl TO d^v tov ttvkvov eKpiekfj elvau 25 

I M V B TOV fjfiiToyialov post fi ponit H 5 dvvificya 

M H : dvvdjj.€da rell. 6 8k om. R 8 rb jBapv] rb supra lin. 

add Me (?}: om. S Kal ini rb 0apb post Kal ini rb o^b ponit H 
10 8ri H : om. rell. 12 ry ante 8ir6y^ add. R 13 rb om. B 
o’vjuff'iiireTai'] fiixrcrai in ras. Ma 15 Spl^eo S 17 aur^v supra 

lin. add. B niKvd B 18 r6vov Meibom : rovrov codd. 

diToviaiov iK/JLcXri ex biroviaiop injuLcX^s Me: biroviouov iKfi€\^s VSB 
21 ini supra lin. add. B rb avrb post ni\iv ponit H 22 avr^v 
in marg. add. B ncacirai post 0apvraros ponit H 24 r6vov 

Meibom : robrov eodd. 


’Er btaroviD be tovov ecf)^ eKorepa rnxiTOViov ov fjLeXiabeLTai. 
^vyL^TicreTai yap | prjTe roits rerdprovs t&v e^s bia Teaadpoov 
(rvp(l)(t)veTv /XTjre rovs Trepirrovs bta irevre. Avo be t6v(^v 
77 Tpi&v fipLTOViov 6^’ eKarepa /xeAwSetrat* (rvfKfxov'qo’ovo’i 
5 yap ^ ol Teraprot bta Te(ro‘d\poi)V rj ol 7 rep. 7 rrot bth nevre. 

[’Atto riptrovLOv pev eirl to 6 ^ bvo obol koX em to ^apv 
6vo,] dirb be tov biTOVov bvo pev eirl to d^, pta 6’ eirl to 
fiapv. AebetKTat yap eirl pev to | d^ TrvKvbv TeOetpevov 
Kal Tovosy TrXetovs be tovt(ov ovk ea’ovTat obol dirb tov 
10 elpripevov biaaTrjpaTOS eirl to o^v* [6776 be to ^apv ttvkvov 
povov,] XeineTai pev yap t&v aavvOeTCjav to blTOVov povov* 11 
bvo be btTova e^s ovKeTt TtOeTat. cSore br]\ov otl bvo povat 
obol eo’ovTat dm tov biTOVov eitl rd d^* 6776 86 rd ^aplv pta* 
bebetKTat yap, otl ovTe biTOvov | irpos btTOVto TeOrjaeTat ovre 
15 Tovo^ 6776 rd ^apv btTovov, coare XetTreTat to ttvkvov. (f>avepbv 
brj OTL dm btTovov eirl pev rd o^v bvo obot, fj pev eirl tov tovov 

Tj 0 6776 TO TTVKVOV, 6776 06 TO papV pta, Tj 6776 | TO TTVKVOV. 

^Atto ttvkvov 8’ evavTL(os 6776 pev rd ^apv bvo oboC, 6776 
86 rd d^ pta. AebetKTat yap dTTO ttvkvov 6776 rd fiapv 86 - 
20 TOVOV TeOetpevov Kal tovos* Tptrr] 8’ ovk | eaTat obos, 
XetTTeTat pev yap t&v davvOeTcov rd ttvkvov, bvo be ttvkvcl 
e^s ov TtOeTat, coaTe 8 ^ Aoz ; otl povat bvo obol eaovTat dTTO 

I StarJi'oi; M V B S r^fi'oi; Meibom; codd. 2 trufifi^furcrai 
Marquard : a’vjj.Trca’cirai codd. 3 a’vjj.<f>($jp€?v in marg. add. B rap 
e^rjs post TTCfivTovs add. H 5 prius fjroi H dia T€<r<rdp($jp ex 
did TcrdpTov Me: did rerdprov V S B 6 ^Airh . . . 5 iJo seclusi 

fi€p^ oif fxkv S d^o 6 do\ ex d 6 o 5* ot Me : dvo 5* ot V S B Kal in 
marg. Me Kal iirl rh fiaph . . . fiia d* om. V S B 7 dwb de tov 

dirdpov . • • eirl rb fiapv in marg. Me 8 dib ante dcdciKrai add. 

Vb S B ydp add. Me : om. V S B rcBcificpop] reSriTai R : 
Tidcficvov H lo iirl . , . fiovov supra lin. in marg. superior! 

add. Me: om. VBS ii dirovov (post t litt. a eras.) M ; did- 

TOVOV VBS 13 ante 6 dol add. H 14 Srt oure] dTi 

ovdev H : oti ovde M V B S 15 <f>av€pbv d'fi Marquard : eSpov 

db eodd. 17 fxiav M V B S 19 ttvkvov ex o^b Me : VBS 

20 Tidc/uLcvov H 22 ov TidcTai • • . fiapb, iirl om. R dvo post 

Sdol ponit S 65 ol post HcovTai ponit H 

III. 66 









III. 67 


iroKvov liii ro ^apv. eTrt Se to o^v juita {fj) ^iri to hhovov 
20 OVT€ yap I 7TVKVOV TTpOS 7TVKV& TlOeTai OVT€ TOVOS 6771 TO 
O^V TTVKVOVy &CrT€ k€LTT€Tat TO hvTOVOV. ^aV€pbv 6^ OTL OTTO 
TTVKVOV 6776 p€V TO fSapV dvO oSot, Tjf T€ 6776 (tOp) TOVOV Kol 
25 Tj 6776 ro btTOVOVy 6776 §6 TO O^V /X6a, | ^ 6776 TO blTOVOV. 

’A770 86 TOVOV pta 6<^’ kK^Tepa obos, 6776 pev to ^apv 

6776 ro biTOVOV 6776 86 rO 0^8 6776 rO TTVKVOV. ’E776 p€V 
30 ro l^apv bebeiKTai ore o{!r6 rwosr re06ra6 | oi;r6 ttvkvov, 
wcrre A66776ra6 ro bOrovov* 6776 86 ro o^i; bebeLKTai ore oi;r6 


Tovos TiOeTai ovt€ btTovovy ^(TTe A66776ra6 ro ttvkvov. ^ave- lo 
pov or) OTi arto tovov fxia €<p (Karepa ooos, em p.€V to papv 

68 6776 ro 8froi;OZ;, || 6776 86 ro O^ 6776 ro TTVKVOV. 

^OpoLios 8’ 6^66 Ka6 6776 T&v xpcdpaTOdV ttX!^v TO y€ pearjs 
5 Kal kiyavov bidirTrjpa peToXapfidveTat dvTt bvrovov ro | y6- 
yvopevov KaO^ kKdaTrjv yjpoav koto, to tov ttvkvov peyeOos. 15 
^Opo((ji)S 8’ 6^66 Kal 6776 TO^V biaTOVCOV 0770 ydp TOV KOLVOV 
TOVOV T<ov yev&v pCa 6(rra6 6</)’ 6Kar6pa 0809, 6776 pev ro 
10 I3apv 6776 ro pearjs Kal Xl^clvov | bidaTripa 8 ti dv ttot€ 
Tvyxdvrj 6v KaO^ eKdcrTYjv yjpoav tQv biaTovoiv, €ttI be ro 0^8 
6776 ro TrapapeoTjs Kal TptTrjs. 20 

^H8?j 86 reoe Kal tovto to TrpdpXrjpa Trapeaye TrXdvrjv* 

15 OavpA^oviTL ydp | tt&s ovyl TOvvavTiov avp^atver aTretpoL 
ydp TLves avTOLS (l>aivovTai eXvai bbol 6^’ 6Kar6pa roS Tovovy 
eTTeibrjTTep tov t€ piaris Kal Xiyavov bLaaTrjpaTOs aTreipa 

I of^] TOV o|i> S rj restituit Westphal dh ante rh dlrovoy 
add. R 2 cIt6 tSpos in marg. B 35^ Marquard : Se codd. 

4-6 TTVKVOV . . . airh dc om. H 4 tov restituit Marquard 5 fj 
om. B €Tr\ de SItovov R cttI Se . . . diTovov in marg. add. Me Vb 
(nisi quod ^ om. Me) ^ om. R 6 airb Sb t6vov fila add. 

in marg. MeVb: om. VS 7-12 M fiiv . . . irvKvbv om. H 

8 TTvKvSv] biTOVOV R lo TidcTai om. R post Tiderai 10 litt. eras. 
M \€\€iTrTai R II 5 ^] Se M V S B 14 biTbvov^ 8i 

t6vov R 15 Korh, R : Kal rell. 18 supra lin. add. Me: 

om. VSB jj.€(rris Kal om. R Kal supra lin. add. Me: om. 
V B S 19 Tvyx<liv€i B S bvrSvosv B 20 bidcTTrifia post 

Tphris add. H 24 re om. S 



fieyeOrj (l>aivovTai ^Xvai tov re ttvkvov | axravTcos. Tlpos 8^ 
ravra Trp&TOv pkv tovt^ ort ovbev piaXkov em tov- 

TOV TOV TrpopXrjpLaTos eTrtjSAex/retez; av tls tovto ^ em tQv 
TT poTepcov. brjXov yap otl Kal tQv airb tov ttvkvov ttjv 
5 ere|paz; t&v db&v airnpa pieyeOr] (TvyL^ricT^Tai XapL^dveiv Kal 
T&v diTO TOV biTovov [8’] oi>(ravT(os [wy]* to re yap tolovtov 
bLaaTTjpLa olov to pLeorjs Kal Xl^clvov airetpa XapL^dveu pLeyeOrj 
TO re TOLOVTOV OLOV I ro ttvkvov TavTo TrdoyeL TrdOos t& 
epiTTpoaOev €lpr]pL€V<o 86a(rr?j/xar6, dX)C opicos ovbev tjttov otto 
lo re TOV TTVKVOV bvo ylyvovTaL obol em ro ^apv kol otto tov 
bLTovov em ro o^v, ^aavT (09 be Kal otto roi; tovov piia 
ytyveTaL e(f>^ eKdTepa 6809. || Ka 0 ’ eKdaTrjv yap ypoav e^’ 
eKdcTTov yevovs XrjTTreov eaTl tcls obovs* beL yap eKacTTov 
TO}V ev Trj pLovaLK^ Kad^ o TreTrepaaTaL KaTa tovto TLOevaL 
15 re Kal TdTTeLV els [ ray eTrto-rTj/xay, fj 8’ direLpov eaTLV edv. 
KaTa piev ovv to, pLeyeOrj t&v 86ao-r?j/xara)z; koX ray t&v 
( f> 66 yy(ov TdcreLS direLpd ttcos (paiveTaL eXvaL ra Trepl /xeAoy, 
Kara 8e ray bvvdpieLS Kal KaTa ra e68?j | Kal KaTa ray OeaeLS 
TTeTTepaapAva re kox TeTaypieva. FivOem ovv otto tov 
20 TTVKVOV at obol em ro I 3 apv Trj re bvvdpieL Kal roty etbecTLV 
d>pL(rpLevaL r’ elal Kal bvo piovov tov dpLOpiov, fj piev | yap 
KaTa TOVOV els bLd^ev^LV ayeL to tov (TV(rTrjpLaTos eXbos, fj 
8e Kara OdTepov bLdaTrjpia, o tl b'qTTOT e^^t pieyeOos, els 
(rvva(f>rjv. brjXov 8’ eK tovt(ov otl Kal drro roS tovov piia 
^5 T I eo-rat e^’ eKdTepa obos Kal evbs etbovs (rviTTrjpLaTos 
ahiaL al o‘vvapL(l) 6 TepaL 68ot, r^y 8ta^ev^ea)y. "'Ort 8’ av 

2 i\€x 07 ji] ante x y eras, M ; iKcyx^V V B 6 5 * del. 

Marquard as del. Meibom 7 Xa/mfidvciv fieycdci H 8 Tavrh 
in marg. B, R : avrh relL 10 re Marquard: he codd. ii rod 
om. H 12 ylpcrai {ip€ in ras.) M 13 §6? ydp cKaffroy 

Meibom : did ydp cKderov codd. 14 ante KaS* ras. M TrcTripaarai 
(ttc in ras., fuisse vid. KaSdirep ircpaffrai) M : ircTrcparai R: ircvcpdffdai H 
15 T6 Marquard : yc codd. ^ conieci: cl codd. 20 at Sdol Mar¬ 
quard : 6 do\ at codd. 21 fiivov Meibom : t6vol codd. ydp om. S 

25 T*] ns R 26 <rvvaii<p 6 rcpai (ot suprascr.) H : <rvvafi<l> 6 T€poi M V B S 

III. 68 










III. 69 


rt9 /Ml] Kara [xtav xpoav ivbs yevovs iirix^Lpfi ras airb t&v 
25 biaaTTipLaroiiv obovs imirKO^TreiV dAA’ d/xa Kara Trdaas airdv- 
TO)P T&v yev&v eh direipCav e/xTrecretrat, (l)av€pbv €k re tQv 
elprjpiivoiiv Kal avrov rod irpaypLaros. 

30 ’Ez; xpco/xart be Kal appLovia ttcls | (pOoyyos twkvov pier- 5 
Ilay /xh; yap ^0oyyo9 ev roh elpr]pLevois yeveatv 

ijTOL TTVKVOV /X6p09 Opi^ei ^ TOVOV 7] TL TOiOVTOV otoV TO 

70 M60-7J9 Kol Xlxclvov bid(rTr]pLa. ol piev ovv || rd tov ttvkvov 
piepr] bpi^ovres ovbev beovrai \6yovy (l>avepoi ydp elai 
TTVKVOV pierexovres* ol be rbv tovov Trepiexovres ebetxd^o’av lo 
5 epLTTpoaOev ttvkvov | ^apvraTOi owes d/x^orepof tQv be 
rd koLTrbv 8td(rr?j/xa TTepiexdvT(ov 6 piev ^apvrepos o^Taros 

ebeix^Tl TTVKVOV 6 8’ o^repos ^apwaTos. ‘^12(rr’ eTretb^ 

lo TO(ravTa piev ean piova rd doijv\6eTa, eKaarov 8’ avT&v 
VTrb TOLOVTOiv (l)66yy(ov Trepte^erat &v eKdrepos ttvkvov pier- 15 
6x^6, brjkov OTL TTCLS ^0dyyo9 ev appLOvta Kal xpwMCtrt ttvkvov 
/xere'xet. | 

15 ''Ort be tQv ev ttvkvQ KeipLev(ov i^Qoyyo^v rpeh elcri 
X(opci(>9 pdbiov (TWibeiVy eTreibrjTTep Trpbs ttvkvQ owe TTVKvbv 
TiOerai owe ttvkvov piepos. brjkov yap on bta rawrjv t^v 20 

20 airiav ovk ecrovrai | TrKeiovs tQv elpripievcov x^pctt ^0oyya)z;. 
'^Ort be aTrb piovov rod ^apvrdrov bvo oboC elatv ecf)^ 

eKdrepay aTrb be r&v XonrSiv pita obbs ecf)^ eKdrepay beiKTeov. 

25 ^v be bebeuypievov ev tols epLTrpoaOeVy on | {aTrb ttvkvov em 
rd fiapv bvo oboL eiaiVy rj piev em rbv tovov rj 8’ em rd 25 

I iTrix€ipy ex ivix€ip €7 Me (?) : rell. 7 ttvkvov jj.€pos~\ 

TrvKvo{fjj.€vos V S in marg. B ^ rt] ijroi R 9 Spl^ovres Mar- 

quard : diopl^ovrcs codd. dcovrai post \ 6 yov ponit H 10 t 6 vov^ 
t6ttov R II TOV ante ttvkvov add. R 12 rh supra lin. add. 

Me: om. V BS KoittQv S fiapvr^pos Marquard : fiap^raros eodd. 
o^vraros in marg. add. B 13 6 5’ add. Me : om. VB S o^vrepos 
Marquard : o^^raros eodd. 14 atr^vScTa R : (ritvQ^ra rell. 15 S>v'\ 
T&v B ij.€T€X€is S, B {sed julctcx^i in marg.) 16 drj\ov • . . 

fjL€T€X€i in marg. Me Vb 20 yap om. H 21 post 

<pd 6 yyQ)v ponit H 24 dh supra lin. add. Me : om. V B S aTrb 

. . . 8 b rb restituit Marquard 



III. 70 

bCrovov. eoTL be to) airb ttvkvov bvo obovs ecvat to avTo 
r£ airb tov jSapVTaTov t(op ev t£ ttvkvQ K€Lijl€V(ov bvo obovs 
6776 ro ^apv eXvaiy ovtos yap ecTTiv 6 TTepaCvcov ro ttvkvov* 
ibebeLKTO ovv on otto biTovov 6776 ro o^v | bvo obol elcriVy 30 
5 17 piev 6776 TOV TOVOV f] b^ 6776 TO TTVKVOV* 60T6 §6 TO 0770 

biTovov bvo obovs eivai ro avTo r£ airo tov o^vrepov t&v 
TO biTovov opiCovTcov bvo obovs 6776 ro o^v eXvaiy ovtos yap 

ioTLV 6 Opi^CdV TO II biTOVOV (6776 TO O^. brjXoV 8’ OTi 
6 aVTOS TO biTOVOV im to O^V Opi^OiV KCU 6 to TWKVOV 6776 
lo ro I3apv) ^apvTaTos OiV irvKvoVy ibebencro yap Kal tovto. 
(ZaT eXvat brjXoVy otl airb tov eiprjpievov (l)06yyov bvo obol 
6^’ eKorepa ^crovTai. | 

"'Otl 8’ airb tov o^vtotov pia obbs eKorepay beuKTeov. 5 
’E86866Kro 8’ on airb ttvkvov iirl ro 6^v pia obbs iaTiVy 
15 ov 86 z; 86 btacpepei Xiyeiv airb ttvkvov piav obbv eXvai eirl 
ro o^v ^ 0770 I roi; irepaivovTos avTb (f)66yyov bih ttjv elprj- 10 
pevrjv ahiav iirl t&v epirpoaOev. bebeiKTai 8’ otl Kal airb 
biTovov pia obbs iaTiv iirl ro fBapvy ovbev be 860^6^66 
\eyeiv airb biTbvov piav obbv eXvai eirl | ro ^apv 7] airb tov 15 
20 opiCovTos ovro (f>0byyov bih Ttjv irpoetpripevriv ahiav 8^Aoz; 

86 OTi Kal 6 avTbs eaTi ^0oyyo9 o Te ro bhovov eirl ro 
fiapv opC^cov Kal 6 ro irvKvbv eirl ro 6^ o^roroy cov 
irv\KVov. "'iliTT eXvai (l)avepbv 6K TovT(oVy otl pia obbs ecf)^ 20 
eKaTepa eorai [eirl] tov elprjpevov ^0oyyoo. 

25 ®'0r6 86 KO6 0770 TOV pecrov pia obbs erf)^ eKCLTepa 6o-ro6, 

I 67 rl rh Paph post 6dohs add. H 2 ^apyrdrov rav ex fiaph 

ToiiTtav Me : ^aph Toi)T(av V S B 36 ir^palvoDV {al in ras., fiiisse 

vid. € et supra lin. ras.) M : ov€p kvav VS, B (sed alvav in marg.) 

4 6$6$et/ci^6iT0 B, sed in marg. idcdciKro dvo post SSol ponit B 

5 TO OTTO R : rd dwo rell. 6 diroyov Meibom : rdyov codd. too 

om. R 7 oStos] ut in ras. Ma 8 ivl . . . fiaph restituit 

Marquard 10 Kal supra lin. add. corn B 15 tov ante ttvkvov 
add. H 19 TOV ante diTovov add. R 21 6 avrJy] 6 om. M V 
S B re] Ti R 22 6 om. M V B R 24 iirl seclusi: ^ciktcov 
M eras. S: dirh Marquard iirl . . . eerrot om. R 



I 61 

III. 71 


25 b€iKT€OV. ’ETTet Toivvv | CLvayKOLOV ix€V T&v rpi&v aavv- 
d€T(ov €V TL {irpos) T<o elpTjpLevio (f) 66 yy(o TiOecOaiy VTTap\€i 
be avTov Ketpievri btecTLS 6^’ eKarepa, brjXov otl ovre btrovov 
30 Te 6 rj(reTaL irpbs avrQ Kar ovberepov r&v roTTOiv | ovre 
Tovos. btrovov yap ovro) rtOepievov rjrot ^apvraros ttvkvov 5 
rj o^vraros Treo-etrat em Trjv avrrjv rdatv r£ elprjpievia 
(fyOoyyip pteatp ovrt ttvkvov^ (Sore ytyveaQat rpets bteaets e^rjs 
72 OTTorepois av reOfj rb btrovov r&v roTrcov rovov {be) 
reOetpievov rb avrb (TvyL^riaerat^ ^apvraros yap ttvkvov 
TT eaetrat eirl rrjv avr^v rdatv pteato ttvkvov, (Sore rpets 10 
5 bt\e(rets e^rjs rtOeaOat. rovrcjav 8* eKpLeX&v ovrodv brjXov 
ort pita bbbs ecj)^ eKarepa earat dirb rod elprjpievov ^^oyyov. 
''On ptev ovv ctirb {rod l^apvrdrov) r&v ^^oyycoz; r&v ev 
10 nvKvCd Ketpievcov bvo e(f> eKd\repa eaovrat oboi dirb be rQv 
XotTT&v eKarepov pita eKdrepa ear at 6809, (I)avep 6 v. 15 
"On 8’ ov reOrjaovrat bvo ^ 0 oyyo 6 dvoptotot Kara rrjv 
15 rod TTVKVod pieroy^v | eiii rrjv avrrjv rdatv epipteXm^ bet- 
Kreov. Tt 6 ea 6 (jCi yap TrpQrov o r’ o^vraros Kal 6 ^apvraros 
erii rrjv avrrjv rdatv* avjx^rjaerat 8^ rovrov ytyvojxevov 
20 bvo TTVKva e^rjs rtOeaOat. rovrov 8’ eKjxekods | ovros eKjxekes 20 
rb TTtirretv {errt rrjv avrrjv rdatv rovs Kara ravrrjv 
rrjv bta(l)opav dvoptotovs) ev ttvkv^ (f> 66 yyovs. ArjXov 
8’ on ov8’ ot Kara rrjv Xet'nojievrjv bta(l>opdv dvdjxotot ^ 0 oyyot 

2 %v\ €v S TTphs restituit Meibom 4 avr^ Meibom H : avrh 

rell. T^TTwi' conieci : Tp6Tra)v codd. clpri/jL^vcov ante Tp6TrcDv add. 

H 5 t6vos diTovov. oUto) yhp M V S B, nisi quod diarSyov (cum 

duobus punclis sub a) B 6 clprjfieycp (pBoyycp Meibom, et /x€<rcp 
Marquard : tcjv €lpruj.€V($>v <p66yy($jv fiiffov codd. 8 rav rSirav 

conieci: codd. 5^ coniecit Meibom iirl Be ante et 

avT^ ante tott^ add. Marquard 10 avr^v • . . &<rT€ om. R 

Meibom; jmcffov codd, aJerre Marquard : wscodd. ii ^rjs 
rldcadai^ ylvcaSai c^rjs H 5 * Marquard : 5 )) codd. 12 jj.ia supra 
lin. add. corr. B 13 rod Papvrdrov restituit Meibom 15 iffrai 
ante i<p' cKarcpa ponit H 18 Tidiffdos . . . r^v avr^v rd^iv in 

marg. S 6 (ante fiapvTaros) H : om. rell. 20 ifjLficXhs 

M V B 21 iir\ T^v . • . avofxolovs addidi 23 8* om. B dyd- 

jLLoioi Marquard ; 81x0101 codd. 



rrjs avTTjs racrem e/xjuteXcS? Koivotivrjirovar rpets yap avayKoiov 
T[\0€(r6aL bteaeLS idv re jSapvTaro^ idv t o^vraros 25 

pi€(r(p rrjs avrrjs pLerdcryip rdcrea)?. 

^Oti be TO bidrovov ovyKeirai t^tol €k hvolv rj Tpt&v rj 

5 T€(T(Tdp(OV d(TVV\6€T(OV, b€iKT€OV* "'OtL pi€V OVV €K TOaOVTCOV 30 

irkeiOTCdv d(rvv0€T(ov eKaarov r&v yev&v (rwearYjKos ecrriv 
{oao) iv tQ bib. irevre, bebeiKTat irporepov ean be Tav\\Ta 73 
reacrapa tov dpL0pi6v. eav ovv t&v recrcrdpoiv rd piev rpia 
Xaa yevryrai to be (reraproz;) dviaov — {tovto be) yiyveTai 
10 ev (TVVTovoiiTdTCd btaTovip —, bvo eorat pLeye0ri pova e^ 

&v TO I bidTovov (TVve(rTr]Kos eorar eav be Ta pev bvo laa 5 
rd be bvo aviaa Trjs TTapvTTdTrjs eirl to ^apv KLvri0eC(rris, 

Tpia eorai pLeye0ri e^ &v to bidTOvov yevos avveaTriKos 
ecTTaiy TO T ekaTTOV r]pLiTo\iKOv koi tovos koI to petCov 10 
1 5 Tovov eav be irdvTa Ta tov bib irevTe pLeye0r] aviaa yevrjTai, 
Tecraapa eorat pLeye0ri {e^ Sv) to elprjpievov yevos eorat 
(TUveaTriKos. "'ilo'T elvai (f>avepov on rd bidTovov | ^rot 15 
6 K bvoiv ^ TpiSiv ^ Teacrdpcjav d(rvv0eT(jdv crvyKeiTai. 

''On be {to) yj)&pia Kal rj appovla ijTOi eK Tpi&v ^ 6k 
20 Teairdpcov aijyKeiTai, beiKTeov. "'Ovtcov be t&v pev {tov) 
bib irevTe d(Tvv\0eT(ov Teo-adpcov tov dpi0pLbv ebv piev Tb 20 
TOV TTVKVov pipT] i(Ta if, Tpla e(TTai peye0ri e^ &v rd elpr]- 
peva yevT] avveaTriKOTa ecrrat, to re roC ttvkvov pepos o 
Ti av fj Kal Tovos Kal to TOiovTov olov pearjs Kal | ki^avov 25 
25 bidaTTjpa. ebv be rd roC ttvkvov pepr] avara fj, Teaaapa 

I Koiv'fia’ovffi B 3 ri(T€(as in marg. B : (rriffcoss rell. 4 jjrot] 

^ H ^vo7v ^ rpiQv Meibom : rpicjv ^ dvoip codd. 5 a<r{fv6€Tov 
M V B S 6 affvvdcrov H 7 5 <ra restituit Meibom 9 rh 
d€ reraproy tiyiiroy — tovto de ylyycTai Marquard : Bh Iffoy ycyriTai 

codd. (nisi quod ycyriTai om. H) 10 diaT 6 y(p om. R 14 7 ifjLiT 6 yioy 
M V B S 16 juLcycdci H ef &y restituit Meursius 18 dvo7y 
Marquard : dvo codd. 19 restituit Marquard e/c ante Tca’o’dpcoy 
om. VBS 20 Se] jj.€y ody H tov restituit Marquard 21 Toy 
corr. ex tcd S 22, 23 ficprj . . . irvKyov om. R 22 ^ B 

23 o’vyea’TTiKdTa Meibom : <rvy€<rTrjK 6 s codd. jiipovs V B S 

24 ante T6yos add. VS ' ' 


M 2 


eorat /xeyeOr] &v ra elprjfjieva yevrj ovvecTTriKOTa earaty . 
kkayicTTOV [JL€V TO TOiovTOv oXov TO viTaTYjs Kol TTapVTTdrqs, 

30 bevTepov 8’ olov ro TrapvTraTrjs Kal Xiyavovy TpiTov bie ro|z;o9, 
T€TapTov be ro tolovtov olov to pLearjs Kal Xtyavov. 

^H8?j be TLS rjiropriire bua tl ovk av Kal Tavra ra yevrj 5 
74 €K 8vo d(TVv 6 eT(ov || etrj crvveaTriKOTa &(nTep Kal to biaTOvov. 
^avepbv b^ tls eart TravTekQs Kal eiTLTTokrjs fj ahia tov 
5 /^V yiyveaOai roCro* Tpia yap daijvOeTa taa e^rjs ev appLO^vta 
piev Kal \p(apLaTL ov rt^erat, ev bLaT 6 v(p be TiOeTau. bta 
TavTr\v 8^ t^v aiTiav ro biaTOVov [xovov eK bvo d(rvv 6 eT(ov 10 
(rvvTiOeTai Trore. 

10 Mera be TavTa XeKTeov tl eaTL Kal \ iroia tls fj KaT 

66809 bLa(l)opd — bLa(l>epeL 8’ rjpLLV ovbev 61809 XeyeLv fj (ryrjpiay 
(l)epopiev yap dpL(l) 6 Tepa to, ovopLOTa tovto eirl ro avTo. 

15 r6yz;6ra6 8’ otov tov ovtov pieyeOovs eK t&v avrQv d\(rvv- 15 
OeTcov ovyKeLpievov pieyeOeL Kal dp60/x£ fj rd^69 avT&v 
dWoLCdOLV kd^rj. Tovtov 8’ ovt(os dcfycdpLapievov tov bLo 
Teaadpcdv otl Tpia etbrjy beLKTeov. TTp&TOV piev ovv ov ro 
20 TTVKVov 6776 ro | /SapVy bevTepov 8’ ov bCeoLS ecj)^ eKdTepa 

86roz;oi;. otl 8’ ovk evbex^TOL Trkeovax&s TeOrjvoL rd roi; 

25 860 TeoadpoiiV piepr] irpos dkkrjka fj | ToaavToy&Sy pcpLOv 


I iffrai om. H <rvv€<rTrjKhs MR 7 5 ))] 5 * et S iirl iroWrjs 
V B S R 8 verba iv apixovlcf. et quae sequuntur omnia in marg. 

add. Me: in V scripta sunt a Vb vel manu diversa a Va, paullo 
iuniore €vapix6via S g ov ante riderai prius om., et ov ante 

rlBcrai alterum add. H 9-11 . . . irore om. H 10 rd 

didroyoy om. R /j.6pov €K Svo Marquard: e/c 5 iJo n6v(av codd. 

12 M B R : rls V S iffri om. V 13 ^ixiv post ovBhv ponit H 
15 dffvvO^Toov ex affvvdirov corr. V: davvQirov S 16 <rvyK€i/j.€Pov 

H S : (TvyKcifiivoiv M R, V (ex ovyKeijmcvov corn) koI ante jmcycdci 
add. M VB S H 17 oKiKoaiv B dWoiaxriv post \dpr} ponit H 

rod 5 ’ oVreos, sed rov et oif in ras. corr. V a<popi(Tfi€vov H : d^opifffi^vov 
B 18 €’l[dri\^dri B o§] ov S 19 o§] ov S 20 ov] ov S 
22 Tca’O’dpQDv] TcrdpTov V B 





The branch of study which bears the name of Harmonic i. 
is to be regarded as one of the several divisions or special 
sciences embraced by the general science that concerns 
itself with Melody. Among these special sciences Harmonic 
occupies a primary and fundamental position; its subject 
matter consists of the fundamental principles — all that 
relates to the theory of scales and keys; and this once 
mastered, our knowledge of the science fulfils every just 
requirement, because it is in such a mastery that its aim 
consists. In advancing to the profounder speculations 2 
which confront us when scales and keys are enlisted in the 
service of poetry, we pass from the study under consideration 
to the all-embracing science of music, of which Harmonic 
is but one part among many. The possession of this greater 
science constitutes the musician. 

The early students of Harmonic contented themselves, as 
a matter of fact, with being students of Harmonic in the 
literal sense of the term; for they investigated the enhar¬ 
monic scale alone, without devoting any consideration to the 
other genera. This may be inferred from the fact that the 
tables of scales presented by them are always of enharmonic 
scales, never in one solitary instance of diatonic or chromatic; 
and that too, although these very tables in which they con- 

^ The references throughout the translation are to Meibom’s edition. 



fined themselves to the enumeration of enharmonic octave 
scales nevertheless exhibited the complete system of 
musical intervals. Nor is this the sole mark of their im¬ 
perfect treatment. In addition to ignoring diatonic and 
chromatic scales they did not even attempt to observe the 
various magnitudes and figures in the enharmonic as well as 
in the other genera. Confining themselves to what is but 
the third part of that complete system, they selected for 
exclusive treatment a single magnitude in that third part, 
namely, the Octave. Again, their mode of treating even 
branches of the study to which they did apply themselves 
was imperfect. This has been clearly illustrated in a former 
work in which we examined the views put forward by the 
students of Harmonic; but it will be brought into a still 
clearer light by an enumeration of the various subdivisions 
of this science, and a description of the sphere of each. We 
3 shall find that they have been in part ignored, in part in¬ 
adequately treated ; and while substantiating our accusations 
we shall at the same time acquire a general conception of 
the nature of our subject. 

The preliminary step towards a scientific investigation of 
music is to adjust our different notions of change of voice, 
meaning thereby change in the position of the voice. Of 
this change there are more forms than one, as it is found 
both in speaking and in singing; for in each of these there 
is a high and l<m, and a change that results in the contrast 
of high and low is a change of position. Yet although this 
movement between high and low of the voice in speaking 
differs specifically from the same movement in singing, no 
authority has hitherto supplied a careful determination of 
the difference, and that despite the fact that without such 
a determination the definition of a note becomes a task very 
difficult of accomplishment. Yet we are bound to accomplish 

it with some degree of accuracy, if we wish to avoid the 


blunder of Lasus and some of the school of Epigonus, who 
attribute breadth to notes. A careful definition will ensure 
us increased correctness in discussing many of the problems 
which will afterwards encounter us. Furthermore, it is 
essential to a clear comprehension of these points that we 
differentiate distinctly between tension and relaxation, height 
and depth, and pitch—conceptions not as yet adequately 
discussed, but either ignored or confused. This done, we 
shall then be confronted by the question whether distance on 4 
the line of pitch can be indefinitely extended or diminished, 
and if so, from what point of view. Our next task will be 
a discussion of intervals in general, followed by a classifica¬ 
tion of them according to every principle of division of which 
they admit; after which our attention will be engaged by 
a consideration of the scale in general, and a presentation 
of the various natural classes of scales. We must then 
indicate in outline the nature of musical melody— musical, 
because of melody there are several kinds, and tuneful 
melody—that which is employed in musical expression—is 
only one class among many. And as the method by which 
one is led to a true conception of this latter involves the 
differentiation of it from the other kinds of melody, it will 
scarcely be possible to avoid touching on these other kinds, 
to some extent at least. When we have thus defined musical 
melody as far as it can be done by a general outline before 
the consideration of details, we must divide the general class, 
breaking it up into as many species as it may appear to 
contain. After this division we must consider the nature 
and origin of continuity or consecution in scales. Our 
next point will be to set forth the differences of the musical 
genera which manifest themselves in the variable notes, 
as well as to give an account of the loci of variation of 
these variable notes. Hitherto these questions have been 
absolutely ignored, and in dealing with them we shall be 



compelled to break new ground, as there is in existence no 
previous treatment of them worth mentioning. 

5 Intervals, first simple and then compound, will next 
occupy our attention. In dealing with compound intervals, 
which as a matter of fact are in a sense scales as well, we 
shall find it necessary to make some remarks on the synthesis 
of simple intervals. Most students of Harmonic, as we 
perceived in a previous work, have failed even to notice 
that a treatment of this subject was required. Eratocles 
and his school have contented themselves with remarking 
that there are two possible melodic progressions starting 
from the interval of the Fourth, both upwards and down¬ 
wards. They do not definitely state whether the law holds 
good from whatever interval of the Fourth the melody 
starts; they assign no reason for their law; they do not 
inquire how other intervals are synthesized—whether there 
is a fixed principle that determines the synthesis of any 
given interval with any other, and under what circumstances 
scales do and do not arise from the syntheses, or whether 
this matter is incapable of determination. On these points 
we find no statements made by any writer, with or without 
demonstration; the result being that although as a matter 
of fact there is a marvellous orderliness in the constitution of 
melody, music has yet been condemned, through the fault 
of those who have meddled with the subject, as falling into 
the opposite defect. The truth is that of all the objects to 
which the five senses apply not one other is characterized 
by an orderliness so extensive and so perfect. Abundant 
evidence for this statement will be forthcoming throughout 
our investigation of our subject, to the enumeration of the 
parts of which we must now return. 

6 Our presentation of the various methods in which simple 
intervals may be collocated will be followed by a discussion 
of the resulting scales (including the Perfect Scale) in which 



we will deduce the number and character of the scales from 
the intervals, and will exhibit the several magnitudes of scales 
as well as the different figures, collocations, and positions pos¬ 
sible in each magnitude ; our aim being that no principle of 
concrete melody, whether magnitude, or figure, or colloca¬ 
tion, or position shall lack demonstration. This part of our 
study has been left untouched by all our predecessors with the 
exception of Eratocles, who attempted a partial enumeration 
without demonstration. How worthless his statements are, 
and how completely he failed even in perception of the facts, 
we have already dwelt upon, when this very subject was the 
matter of our inquiry. As we then observed all the scales 
with the exception of one have been completely passed over; 
and of that one scale Eratocles merely endeavoured to 
enumerate the figures of one magnitude, namely the octave, 
empirically determining their number, without any attempt 
at demonstration, by the recurrence of the intervals. He 
failed to observe that unless there be previous demonstration 
of the figures of the Fifth and Fourth, as well as of the laws 
of their melodious collocation, such an empirical process 
will give us not seven figures, but many multiples of seven. 
Further discussion here is rendered unnecessary by our 
previous demonstration of these facts; and we may now 
resume our sketch of the divisions of our subject. 

When the scales in each genus have been enumerated in 
accordance with the several variations just mentioned, we 
must blend the scales and repeat the process of enumera¬ 
tion. The necessity for this investigation has escaped most 
students; nay, they have not so much as mastered the true 
conception of ‘ blending.’ 

Notes form the next subject for inquiry, inasmuch as 
intervals do not suffice for their determination. 

Again, every scale when sung or played is located in 
a certain region of the voice; and although this location 



induces no difference in the scale regarded in itself, it im¬ 
parts to the melody employing that scale no common—nay 
rather perhaps its most striking characteristic. Hence he 
who would deal with the science before us must treat of the 
‘ region of the voice ’ in general and in detail so far as is 
reasonable ; in other words so far as the nature of the scales 
themselves prescribes. And in dealing with the affinity 
between scales and regions of the voice, and with keys, we 
must not follow the Harmonists in their endeavour at com¬ 
pression, but aim rather at the intermodulation of scales, by 
considering in what keys the various scales must be set so 
as to admit of intermodulation. We have shown in a previous 
work that, though as a matter of fact some of the Harmonists 
have touched on this branch of our subject in a purely 
accidental way, in connexion with their endeavour to exhibit 
a close-packed scheme of scales, yet there has been no 
general treatment of it by a single writer belonging to this 
8 school. This position of our subject may broadly be 
described as the part of the science of modulation con¬ 
cerned with melody. 

We have now set forth the nature and number of the 
parts of Harmonic. Any investigations that would carry us 
further must, as we remarked at the outset, be regarded 
as belonging to a more advanced science. Postponing 
accordingly to the proper occasion the consideration of 
these, their number, and their several natures, it now 
devolves upon us to give an account of the primary science 

Our first problem consists in ascertaining the various 
species of motion. Every voice is capable of change of 
position, and this change may be either continuous or by 
intervals. In continuous change of position the voice 
seems to the senses to traverse a certain space in such a 
manner that it does not become stationary at any point, not 


even at the extremities of its progress—such at least is the 
evidence of our sense-perception—but passes on into 
silence with unbroken continuity. In the other species 
which we designate motion by intervals, the process seems 
to be of exactly the opposite nature: the voice in its 
progress stations itself at a certain pitch, and then again at 
another, pursuing this process continuously—continuously, 
that is, in time. As it leaps the distances contained 
between the successive points of pitch, while it is stationary 
at, and produces sounds upon, the points themselves, it 
is said to sing only the latter, and to move by intervals. 
Both these descriptions must of course be regarded in the 9 
light of sensuous cognition. Whether voice can really 
move or not, and whether it can become stationary at 
a given point of pitch, are questions beyond the scope of 
the present inquiry, which does not demand the raising 
of this problem. For whatever the answer may be, it does 
not affect the distinction between the melodious motion 
of the voice and its other motions. Disregarding all such 
difficulties, we describe the motion of the voice as con¬ 
tinuous when it moves in such a way as to seem to the 
ear not to become stationary at any point of pitch; but 
when the reverse is the case—when the voice seems to the 
ear first to come to a standstill on a point of pitch, then to 
leap over a certain space, and, having done so, to come to a 
standstill on a second point, and to repeat this alternating 
process continuously—the motion of the voice under these 
circumstances we describe as motion by intervals. Con¬ 
tinuous motion we call the motion of speech, as in speaking 
the voice moves without ever seeming to come to a stand¬ 
still. The reverse is the case with the other motion, which 
we designate motion by intervals: in that the voice does 
seem to become stationary, and when employing this 

motion one is always said not to speak but to sing. Hence 



in ordinary conversation we avoid bringing the voice to a 
standstill, unless occasionally forced by strong feeling to 
resort to such a motion; whereas in singing we act in 

10 precisely the opposite way, avoiding continuous motion and 
making the voice become, as far as possible, absolutely 
stationary. The more we succeed in rendering each of our 
voice-utterances one, stationary, and identical, the more 
correct does the singing appear to the ear. To conclude, 
enough has been said to show that there are two species of 
the voice’s motion, and that one is continuous and employed 
in speaking, while one proceeds by intervals and is 
employed in singing. 

It is evident that the voice must in singing produce the 
tensions and relaxations inaudibly, and that the points of 
pitch alone must be audibly enunciated. This is clear from 
the fact that the voice must pass imperceptibly through the 
compass of the interval which it traverses in ascending or 
descending, while the notes that bound the intervals must 
be audible and stationary. Hence it is needful to discuss 
tension and relaxation, and in addition height and depth of 
pitch, and finally pitch in general. 

Tension is the continuous transition of the voice from a 
lower position to a higher, relaxation that from a higher to 
a lower. Height of pitch is the result of tension, depth 
the result of relaxation. On a superficial consideration of 
these questions it might appear surprising that we distinguish 
four phenomena here instead of two, and in fact it is usual 
to identify height of pitch with tension, and depth of pitch 

11 with relaxation. Hence we may perhaps with advantage 
observe that the usual view implies a confusion of thought. 
In doing so we must endeavour to understand, by observing 
the phenomenon itself, what precisely takes place when in 
tuning we tighten a string or relax it. All who possess even 

a slight acquaintance with instruments are aware that in 


producing tension we raise the string to a higher pitch, and 
that in relaxing it we lower its pitch. Now, while we are 
thus raising the pitch of the string, it is obvious that the 
height of pitch which is to result from the process cannot 
yet be in existence. Height of pitch will only result when 
the string becomes stationary and ceases to change, after 
having been brought by the process of tension to the point 
of pitch required; in other words, when the tension has 
ceased and no longer exists. For it is impossible that a 
string should be at the same moment in motion and at rest; 
and as we have seen, tension takes place when the string 
is in motion, height of pitch when it is quiescent and 
stationary. The same remarks will apply to relaxation and 
depth of pitch, except that these are concerned with change 
in the opposite direction and its result. It is evident, then, 
that relaxation and depth of pitch, tension and height of 
pitch, must not be identified, but stand to one another in 
the relation of cause and effect. It remains to show that 
the term pitch also connotes a quite distinct conception. 

By the term pitch we mean to indicate a certain per-12 
sistence, as it were, or stationary position of the voice. 
And let us not be alarmed by the theory which reduces 
notes to motions and asserts sound in general to be a 
motion, as though our definition involved the proposition 
‘that under certain circumstances motion will, instead of 
moving, be stationary and at rest. The definition of pitch 
as a certain condition of motion—call it ‘equability’ or 
‘ identity,’ or by any more enlightening term you can find— 
will not affect our position. We shall none the less describe 
the voice as stationary when our senses assure us that it is 
neither ascending nor descending, simply fixing on this 
term as descriptive of such a state of the voice without any 
further implications. To proceed, then, the voice appears 
to act thus in singing; it moves in making an interval, it is 



stationary on the note. Now if we use the term ‘motion ’ 
and say ‘ the voice moves ’ in cases where, according to the 
physical theory, it undergoes a change in the rate of motion ; 
and if, again, we use the term ‘ rest ’ and say ‘ the voice rests ’ 
in cases where this change in the rate of motion has ceased, 
and the motion has become uniform, our musical theory is 
not thereby affected. For it is plain enough that the term 
‘ motion ’ in the physical sense covers both ‘ motion ’ and 
‘rest’ in the sense in which we employ them. Sufficient 
has been said on this point here; elsewhere it has been 
treated more fully and clearly. 

To resume; it now being clear that pitch is distinct from 
tension or relaxation, the former being, as we say, a rest of 
the voice, the latter, as we have seen, motions, our next 
task is to understand that it is distinct from the remaining 
phenomena of height and depth of pitch. Now, our pre¬ 
vious observations have shown that the voice is, as a matter 
of fact, in a state of rest after a transition to height or depth; 
yet the' following considerations will make it clear that 
pitch, though a rest of the voice, is a phenomenon distinct 
from both. We must understand that for the voice to be 
stationary means its remaining at one pitch; and this will 
happen equally whether it becomes stationary at a high 
pitch or a low. If pitch, then, be met in high notes as well 
as low notes—and the voice, as we have shown, must of 
necessity be capable of becoming stationary on both alike— 
it follows that, inasmuch as height and depth are absolutely 
incompatible, pitch, which is a phenomenon common to 
both, must be distinct from one and the other alike. Enough 
has now been said to show that pitch, height and depth of 
pitch, and tension and relaxation of pitch are five con¬ 
ceptions which do not admit of any identification infer se. 

The next point for our consideration is whether distance 
on the line of pitch admits of infinite extension or diminu- 



tion. There is no difficulty in seeing that if we refer solely 14 
to musical sounds, such infinite extension and diminution 
are impossible. For every musical instrument and for every 
human voice there is a maximum compass which they 
cannot exceed, and a minimum interval, less than which 
they cannot produce. No organ of sound can indefinitely 
enlarge its range or indefinitely reduce its intervals : in both 
cases it reaches a limit. Each of these limits must be 
determined by a reference to that which produces the sound 
and to that which discriminates it—the voice, namely, and 
the ear. What the voice carmot produce and the ear 
cannot discriminate must be excluded from the available 
and practically possible range of musical sound. In the 
progress in parvitatem the voice and the ear seem to fail at 
the same point. The voice cannot differentiate, nor can 
the ear discriminate, any interval smaller than the smallest 
diesis, so as to determine what fraction it is of a diesis or of 
any other of the known intervals. In the progress in 
magnitudinem the power of the ear may perhaps be con¬ 
sidered to stretch beyond that of the voice, though to no 
very great distance. In any case, whether we are to assume 
the same limit for voice and ear in both directions, or 
whether we are to suppose it to be the same in the progress 
in parvitatem but different in the progress in magnitudinem, 
the fact remains that there is a maximum and minimum 
limit of distance on the line of pitch, either common to 15 
voice and ear, or peculiar to each. It is clear, then, that 
distance of high and low on the line of pitch, regarded in 
relation to voice and ear, is incapable of infinite extension or 
infinitesimal diminution. Whether, regarding the constitution 
of melody in the abstract, we are bound to admit such an 
infinite progress, is a question demanding a different method 
of reasoning not required for our present purpose, and we 
shall accordingly reserve its discussion for a later occasion. 



The question of distance on the line of pitch being 
• disposed of, we shall proceed to define a note. Briefly, 
it is the incidence of the voice upon one point of pitch. 
Whenever the voice is heard to remain stationary on one 
pitch, we have a note qualifled to take a place in a 

An interval, on the other hand, is the distance bounded 
by two notes which have not the same pitch. For, roughly 
speaking, an interval is a difference between points of pitch, 
a space potentially admitting notes higher than the lower of 
the two points of pitch which bound the interval, and lower 
than the higher of them. A difference between points of 
pitch depends on degrees of tension. 

16 A scale, again, is to be regarded as the compound of two 
or more intervals. Here we would ask our hearers to 
receive these definitions in the right spirit, not with jealous 
scrutiny of the degree of their exactness. We would ask 
him to aid us with his intelligent sympathy, and to consider 
our definition sufficiently instructive when it puts him in 
the way of understanding the thing defined. To supply a 
definition which affords an unexceptionable and exhaustive 
analysis is a difficult task in the case of all fundamental 
motions, and by no means least difficult in the case of the 
note, the interval, and the scale. 

We must now endeavour to classify first intervals and 
then scales according to all those principles of division that 
are of practical use. The first classification of intervals 
distinguishes them by their compass, the second regards 
them as concordant or discordant, the third as simple or 
compound, the fourth divides them according to the 
musical genus, the fifth as rational or irrational. As all 
other classifications are of no practical use, let us disregard 
them for the present. 

17 In scales will be found, with one exception, all the dis- 



tinctions which we have met in intervals. It is obvious 
that scales may differ both in compass and owing to the 
fact that the notes bounding that compass may be either 
concordant or discordant. The third, however, of the dis¬ 
tinctions mentioned in the case of intervals cannot exist 
in the case of scales. Evidently we carmot have simple 
and compound scales, at least not in the same way as we 
had simple and compound intervals. The fourth dis¬ 
tinction—that according to genera—must also exist in the 
case of scales, some of them being diatonic, some chromatic, 
and some enharmonic. It is obvious that they also admit 
the fifth principle of division: some are bounded by a 
rational, and some by an irrational, interval. To these four 
there must be added three other classifications. First, 
there is that into the conjunct scales, the disjunct scales, 
and the scales that are a combination of both; every scale, 
provided it is of a certain compass, becomes either conjunct 
or disjunct, or else combines both these qualities—for cases 
are to be seen where the latter process takes place. There 
is, secondly, the division into transilient and continuous, 
every scale belonging to one category or the other; and 
finally, that into single, double, and multiple, as all without i8 
exception admit of classification under these heads. An 
explanation of each of these terms will be given in the 

Starting from these definitions and classifications we 
must seek to indicate in outline the nature of melody. We 
have already observed that here the motion of the voice 
must be by intervals; herein, then, lies the. distinction 
between the melody of music and of speech—for there is 
also a kind of melody in speech which depends upon the 
accents of words, as the voice in speaking rises and sinks 
by a natural law. Again, melody which accords with 
the laws of harmony is not constituted by intervals and 

N 177 



notes alone. Collocation upon a definite principle is also 
indispensable, it being obvious that intervals and notes are 
equally constituents of melody which violates the laws of 
harmony. It follows that the most important and signi¬ 
ficant factor in the right constitution of melody is the 
principle of collocation in general as well as its special 
laws. We see, then, that musical melody differs from the 
melody of speech, on the one hand, in employing motion 
by intervals, and from faulty melody, on the other hand, 
melody which violates the laws of harmony, by the different 
19 manner in which it collocates the simple intervals. What 
this manner is will be shown in the sequel; for the present 
it will suffice to insist on the fact that, though melody which 
accords with the laws of harmony admits of many variations 
in collocating the intervals, there is yet one invariable 
attribute that can be predicated of every such melody, of 
so great importance that with its removal the harmony 
disappears. A full explanation will be given in the course 
of the treatise. For the present we content ourselves with 
this definition of musical melody in contradistinction to 
the other species, but it must be understood that we have 
supplied a mere outline without as yet reviewing the details. 

Our next step will be to enumerate the genera into which 
melody in general may be divided. These are apparently 
three in number. Any melody we take that is harmonized 
on one principle is diatonic or chromatic or enharmonic. 
Of these genera the diatonic must be granted to be 
the first and oldest, inasmuch as mankind lights upon 
it before the others; the chromatic comes next. The 
enharmonic is the third and most recondite; and it is only 
at a late stage, and with great labour and difficulty, that 
the ear becomes accustomed to it. 

We shall now return to the second of the distinctions 
in intervals previously enumerated, and shall proceed to 


examine one of the two classes there contrasted. These 
classes consist, as was remarked, of concorcls and discords, 20 
and it is the former that we shall now take for consideration. 

We shall endeavour to establish the facts with regard to one 
of the many points in which concords differ, namely respect 
of compass. The nature of melody in the abstract deter¬ 
mines which concord has the least compass. Though many 
smaller intervals than the-Fourth occur in melody, they are 
without exception discords. But while the least concordant 
interval is thus determined, we find no similar determination 
for the greatest; for as far at any rate as the nature of 
melody in the abstract is concerned, concords seem capable 
of infinite extension just as much as discords. If we add 
to an octave any concord, whether greater than, equal to, 
or less than, an octave, the sum is a concord. From this 
point of view, then, there is no maximum concord. If, 
however, we regard our practical capacities—in other words, 
the capacities of the human voice and of instruments—there 
is apparently such a maximum, the interval, namely, com¬ 
posed of two octaves and a Fifth. The compass of three 
octaves is, as a matter of fact, beyond our reach. We must 
of course determine the compass of the maximum concOrd 
by the pitch and limits of some one instrument. For 
doubtless we should find an interval greater than the above- 
mentioned three octaves between the highest note of the 
soprano clarinet, and the lowest note of the bass clarinet; 
and again between the highest note of a clarinet player 21 
performing with the speaker open, and the lowest note of 
a clarinet player performing with the speaker closed. A 
similar relation, too, would be found to exist between the 
voices of a child and a man. It is, indeed, from cases 
such as these that we come to know the large concords. 
For it is from voices of different ages, and instruments of 
different measurements that we have learned that the interval 

N 2 


of three octaves, of four octaves, and even greater intervals 
than these are concordant. Our conclusion then is that, 
while the smallest concord is given by the nature of abstract 
melody, the greatest is only determined by our capabilities. 

That the concordant intervals are eight in number will 
be readily admitted. . . . 

The determination of the interval of a tone is our next 
task. A tone is the difference in compass between the 
first two concords, and may be divided by three lowest 
denominators, as melody admits of half tones, thirds of 
tones, and quarter-tones, while undeniably rejecting any 
interval less than these. Let us designate the smallest of 
these intervals the smallest enharmonic diesis, the next the 
smallest chromatic diesis, and the greatest a semitone. 

Let us now set ourselves to consider the origin and 
22 nature of the differences of the genera. Our attention 
must be directed to the smallest of the concords, that of 
which the compass is usually occupied by four notes— 
whence its ancient name. [Now since in such an interval 

the notes may be arranged in many different orders, what 


order are we to choose for consideration? One in which 
the fixed notes and the notes that change with the variation 
in genus are equal in number. An example of the order 
required will be found in the interval between the Mese 
and the Hypate: here, while the two intermediate notes 
vary, the two extremes are left unchanged by genus-variation.] 
Let this then be granted. Further, while there are several 
groups of notes which fill this scheme of the Fourth, each 
distinguished by its own special nomenclature, there is one 
which, as being more familiar than any other to the student 
of music, may be selected as that wherein we shall consider 
how variation of genus makes its appearance. It consists 
of the Mese, Lichanus, Parhypate, and Hypate. 



That variation of genus arises through the raising and 
lowering of the movable notes is obvious; but the locus 
of the variation of these notes requires discussion. The 
locus of the variation of the Lichanus is a tone, for this 
note is never nearer the Mese than the interval of a tone, 
and never further from it than the interval of two tones. 
The lesser of these extreme intervals is recognized as 
legitimate by those who have grasped the principle of the 
Diatonic Genus, and those who have not yet mastered it 23 
can be led by particular instances to the same admission. 
The greater of these extreme intervals, on the other hand, 
finds no such universal acceptance; but the reason for 
this must be postponed to the sequel. That there is a style 
of composition which demands a Lichanus at a distance of 
two tones from the Mese, and that far from being con¬ 
temptible it is perhaps the noblest of all styles—this is 
a truth which is indeed far from patent to most musical 
students of to-day, though it would become so if they were 
led to the apprehension of it by the aid of concrete 
examples. But to any one who possesses an adequate 
acquaintance with the first and second styles of ancient 
music, it is an indisputable truth. Theorists who are 
only familiar with the style of composition now in vogue 
naturally exclude the two-tone Lichanus, the prevailing 
tendency being to the use of the higher Lichani. The 
ground of this fashion lies in the perpetual striving after 
sweetness, attested by the fact that time and attention 
are mostly devoted to chromatic music, and that when 
the enharmonic is introduced, it is approximated to the 
chromatic, while the ethical character of the music suffers 
a corresponding deflection. Without carrying this line of 
thought any further, we shall assume the locus of the 
Lichanus to be a tone, and that of the Parhypate to be 

the smallest diesis, as the latter note is never nearer to the 



Hypate than a diesis, and never further from it than a 
semitone. For the loci do not overlap; their point of 
contact serves as a limit to both of them. The point 
of pitch upon which the Parhypate in its ascent meets the 
Lichanus in its descent supplies a boundary to the loci, 

24 the lower locus being that of the Parhypate, the higher that 
of the Lichanus. 

Having thus determined the total loci of the Lichanus 
and Parhypate, we shall now proceed to ascertain their loci 
as qualified by genus and shade. The proper method of 
investigating whether the Fourth can be expressed in terms 
of any lower intervals, or whether it is incommensurable 
with them all, is given in my chapter on ‘Intervals ascer¬ 
tained by the principle of Concord.’ Here we shall assume 
that its apparent value is correct, and that it consists of two 
and a half tones. Again, we shall apply the term Pycnum ^ 
to the combination of two intervals, the sum of which is 
less than the complement that makes up the Fourth. Let 
us now, starting from the lower of the two fixed notes, 
take the least Pycnum: it will consist of the two least 
enharmonic dieses; while a second Pycnum, taken from 
the same note, will consist of two of the least chromatic 
dieses. This gives the two lowest Lichani of two genera— 
the enharmonic and the chromatic; the enharmonic Lichani 
being in general, as we saw, the lowest, the chromatic 
coming next, and the diatonic being the highest. Again, 
let a third Pycnum be taken, still from the same note; then 
a fourth, which is equal to a tone; then fifthly, from the 
same note, let there be taken a scale consisting of a tone 
and a quarter; then a sixth scale consisting of a tone and 
a half. We have already mentioned the Lichani bounding 

25 the first and the second Pycna; that bounding the third is 
chromatic, and the special chroma to which it belongs is 

‘ i. e. ‘close,’ ‘compressed.’ 



called the Hemiolic. The Lichanus bounding the fourth 
Pycnum is also chromatic, and the special class to which it 
belongs is called the Tonic Chromatic. The fifth scale is 
too great for a Pycnum, for here the sum of the intervals 
between the H57pate and Parhypate and between the Par- 
hypate and the Lichanus is equal to the interval between 
the Lichanus and the Mese. The Lichanus bounding this 
scale, is the lowest diatonic. The sixth scale we assumed is 
bounded by the highest diatonic Lichanus. Thus the 
lowest chromatic Lichanus is one-sixth of a tone higher 
than the lowest enharmonic ; since the chromatic diesis 
is greater than the enharmonic by one-twelfth of a tone— 
the third of a quantity being one-twelfth greater than the 
fourth—and similarly the two chromatic dieses exceed the 
two enharmonic by double that quantity, namely one-sixth 
—an interval smaller than the smallest admitted in melody. 
Such intervals are not melodic elements, or in other words 
cannot take an independent place in a scale. Again, the 
lowest diatonic Lichanus is seven-twelfths of a tone higher 
than the lowest chromatic; for from the former to the 
Lichanus of the hemiolic chroma is half a tone; from this 
Lichanus to the enharmonic is a diesis; from the enhar¬ 
monic Lichanus to the lowest chromatic is one-sixth of 
a tone; while from the lowest chromatic to that of the 
hemiolic chroma is one-twelfth of a tone. But as a quarter 26 
consists of three-twelfths, it is clear that there is the interval 
just mentioned between the lowest diatonic and the lowest 
chromatic Lichanus. The highest diatonic Lichanus is 
higher than the lowest diatonic by a diesis. These con¬ 
siderations show the locus of each of the Lichani. Every 
Lichanus below the chromatic is enharmonic, every Lichanus 
below the diatonic is chromatic down to the lowest chroma¬ 
tic, and every Lichanus lower than the highest diatonic is 
diatonic down to the lowest diatonic. For "we must regard 



the Lichani as infinite in number. Let the voice become 
stationary at any point in the locus of the Lichanus here 
demonstrated, and the result is a Lichanus. In the locus 
of the Lichanus there is no empty space—no space incapable 
of admitting a Lichanus. The point we are discussing is 
one of no little importance. Other musicians only dispute 
as to the position of the Lichanus—whether, for instance, 
the Lichanus in the enharmonic species is two tones re¬ 
moved from the Mese or holds a higher position, thus 
assuming but one enharmonic Lichanus; we, on the other 
hand, not only assert that there is a plurality of Lichani 
in each class, but even declare that their number is infinite. 

Passing from the Lichani we find but two loci for the 
Parhypate, one common to the diatonic and chromatic 
genus and one peculiar to the enharmonic. For two of the 
genera have the Parhypate in common. Every Parhy- 
27 pate lower than the lowest chromatic is enharmonic; every 
other down to this point of limitation is chromatic and 
diatonic. As regards the intervals, while that between the 
Hypate and Parhypate is either equal to or less than that 
between the Parhypate and the Lichanus, the latter may 
be less than, equal to, or greater than that between the 
Lichanus and the Mese, the reason being that the two 
genera have their Parhypate in common. We can have 
a melodious tetrachord with the lowest chromatic Parhypate 
and the highest diatonic Lichanus. Enough has now been 
said to show how great is the locus of the Parhypate both 
in respect of its subdivisions and when regarded as a 

Of continuity and consecution it would be no easy task 
to give accurate definitions at the outset, but a few rough 
indications must be offered. Continuity in melody seems 
in its nature to correspond to that continuity in speech which 



is observable in the collocation of the letters. In speaking, 
the voice by a natural law places one letter first in each 
syllable, another second, another third, another fourth, and 
so on. This is done in no random order: rather, the growth 
of the whole from the parts follows a natural law. Similarly 
in singing, the voice seems to arrange its intervals and notes 
on a principle of continuity, observing a natural law of 
collocation, and not placing any interval at random after 
any other, whether equal or unequal. In inquiring into a8 
continuity we must avoid the example set by the Harmonists 
in their condensed diagrams, where they mark as consecutive 
notes those that are separated from one another by the 
smallest interval. For so far is the voice from being able 
to produce twenty-eight consecutive dieses, that it can by 
no effort produce three dieses in succession. If ascending 
after two dieses, it can produce nothing less than the com¬ 
plement of the Fourth, and that is either eight times the 
smallest diesis, or falls short of it only by a minute and 
unmelodic interval. If descending, it cannot after the two 
dieses introduce any interval less than a tone. It is not, 
then, in the mere equality or inequality of successive 
intervals that we must seek the clue to the principle of 
continuity. We must direct our eyes to the natural laws of 
melody and endeavour to discover what intervals the voice 
is by nature capable of placing in succession in a melodic 
series. For if after the Parhypate and the Lichanus the 
voice can produce no note nearer than the Mese, then the 
Mese is the next note to the Lichanus, whether the interval 
between them be twice or several times that between the 
Lichanus and the Parhypate. The proper method of in¬ 
vestigating continuity is now clear; but how it arises, and 
what intervals do and do not form a succession, are questions 29 
which will be treated in the Elements. 

We shall here assume that, having posited a Pycnum or 



a scale that is not a Pycnum, the smallest interval that can 
succeed in the ascending scale is the complement of the 
interval of the Fourth, and that the smallest similarly in the 
descending scale is a tone.. We shall assume that if a series 
of notes be arranged in proper melodic continuity in any 
genus, any note in that series will either form with the fourth 
from it in order the concord of the Fourth, or with the fifth 
from it in order the concord of the Fifth, while possibly 
forming both. A note that answers to none of these tests 
cannot belong to the same melodic series as those with 
which it makes no concord. Further, we shall assume that 
whereas there are four intervals contained in the interval of 
the Fifth, two of which are usually equal, viz. those con¬ 
stituting the Pycnum, and two unequal—one the complement 
of the first concord, the other the excess of the interval of 
the Fifth over that of the Fourth, the unequal intervals 
which succeed the equal intervals do so in different order 
according as we ascend or descend the scale. We shall 
assume too that notes which form respectively the same 
concord with consecutive notes are themselves consecutive ; 
that in each genus a simple melodic interval is one which 
the voice cannot divide in a melodic progression; that not 
all the magnitudes into which a concord can be divided 
are simple; that a sequence is a progression by consecutive 
notes, each of which, between the first and last, is pre¬ 
ceded and succeeded by a simple interval; and that a 
direct sequence is one that maintains the same direction 


It will be well perhaps to review in anticipation the course 30. 
of our study; thus a foreknowledge of the road that we must 
travel will enable us to recognize each stage as we reach it, 
and so lighten the toil of the journey; nor shall we be 
harbouring unknown to ourselves a false conception of our 
subject. Such was the condition, as Aristotle used often to 
relate, of most of the audience that attended Plato’s lectures 
on the Good. They came, he used to say, every one of 
them, in the conviction that they would get from the 
lectures some one or other of the things that the world calls 
good; riches or health, or strength, in fine, some extra¬ 
ordinary gift of fortune. But when they found that Plato’s 
reasonings were of sciences and numbers, and geometry, 
and astronomy, and of good and unity as predicates of the 
finite, methinks their disenchantment was complete. The 31 
result was that some of them sneered at the thing, while 
others vilified it. Now to what was all this trouble due ? 

To the fact that they had not waited to inform themselves 
of the nature of the subject, but after the manner of the sect 
of word-catchers had flocked round open-mouthed, attracted 
by the mere title ‘ good ’ in itself. 

But if a general exposition of the subject had been given 
in advance, the intending pupil would either have abandoned 
his intention or if he was pleased with the exposition, would 
have remained in the said conviction to the end. It was 
for these very reasons, as he told us, that Aristotle himself 

used to give his intending pupils a preparatory statement of 



the subject and method of his course of study. And we 
agree with him in thinking, as we said at the beginning, that 
such prior information is desirable. For mistakes are often 
made in both directions. Some consider Harmonic a 
sublime science, and expect a course of it to make them 
musicians; nay some even conceive it will exalt their moral 
nature. This mistake is due to their having run away with 
such phrases in our preamble as ‘ we aim at the construction 
of every style of melody,’ and with our general statement 
‘ one class of musical art is hurtful to the moral character, 
another improves it ’ 3 while they missed completely our 
qualification of this statement, ‘ in so far as musical art can 
improve the moral character.’ Then on the other hand 
there are persons who regard Harmonic as quite a thing of 
no importance, and actually prefer to remain totally un¬ 
acquainted even with its nature and aim. Neither of these 
views is correct. On the one hand the science is no proper 
object of contempt to the man of intelligence—this we shall 
32 see as the discussion progresses; nor on the other hand 
has it the quality of all-Sufficiency, as some imagine. To 
be a musician, as we are always insisting, implies much 
more than a knowledge of Harmonic, which is only one 
part of the musician’s equipment, on the same level as the 
sciences of Rhythm, of Metre, of Instruments. 

We shall now proceed to the consideration of Harmonic 
and its parts. It is to be observed that in general the 
subject of our study is the question. In melody of every 
kind what are the natural laws according to which the voice 
in ascending or descending places the intervals ? For we 
hold that the voice follows a natural law in its motion, and 
does not place the intervals at random. And of our answers 
we endeavour to supply proofs that will be in agreement with 
the phenomena—in this unlike our predecessors. For some 
of these introduced extraneous reasoning, and rejecting the 


senses as inaccurate fabricated rational principles, asserting 
that height and depth of pitch consist in certain numerical 
ratios and relative rates of vibration—a theory utterly 
extraneous to the subject and quite at variance with the 
phenomena; while others, dispensing with reason and 
demonstration, confined themselves to isolated dogmatic 
statements, not being successful either in their enumera¬ 
tion of the mere phenomena. It is our endeavour that 
the principles w'hich we assume shall without exception 
be evident to those who understand music, and that we 33 
shall advance to our conclusions by strict demonstration. 

Our subject-matter then being all melody, whether vocal 
or instrumental, our method rests in the last resort on an 
appeal to the two faculties of hearing and intellect. By the 
former we judge the magnitudes of the intervals, by the 
latter we contemplate the functions of the notes. We must 
therefore accustom ourselves to an accurate discrimination 
of particulars. It is usual in geometrical constructions to 
use such a phrase as ‘ Let this be a straight line ’; but one 
must not be content with such language of assumption in 
the case of intervals. The geometrician makes no use of 
his faculty of sense-perception. He does not in any degree 
train his sight to discriminate the straight line, the circle, 
or any other figure, such training belonging rather to the 
practice of the carpenter, the turner, or some other such 
handicraftsman. But for the student of musical science 
accuracy of sense-perception is a fundamental requirement. 
For if his sense-perception is deficient, it is impossible for 
him to deal successfully with those questions that lie outside 
the sphere of sense-perception altogether. This will become 
clear in the course of our investigation. And we must bear 
in mind that musical cognition implies the simultaneous 
cognition of a permanent and of a changeable element, and 

that this applies without limitation or qualification to every 



branch of music. To begin with, our perception of the 
differences of the genera is dependent on the permanence 
of the containing, and the variation of the intermediate, 

34 notes. Again, while the magnitude remains constant, we 
distinguish the interval between Hypate and Mese from that 
between Paramese and Nete; here, then, the magnitude 
is permanent, while the functions of the notes change; 
similarly, when there are several figures of the same magni¬ 
tude, as of the Fourth, or Fifth, or any other; similarly, 
when the same interval leads or does not lead to modulation, 
according to its position. Again, in matters of rhythm we 
find many similar examples. Without any change in the 
characteristic proportion constituting any one genus of 
rhythm, the lengths of the feet vary in obedience to the 
general rate of movement; and while the magnitudes are 
constant, the quality of the feet undergoes a change; and 
the same magnitude serves as a foot, and as a combination 
of feet. Plainly, too, unless there was a permanent quantum 
to deal with there could be no distinctions as to the methods 
of dividing it and arranging its parts. And in general, 
while rhythmical composition employs a rich variety of 
movements, the movements of the feet by which we note 
the rhythms are always simple and the same. Such, then, 
being the nature of music, we must in matters of harmony 
also accustom both ear and intellect to a correct judgement 
of the permanent and changeable element alike. 

These remarks have exhibited the general character of 
the science called Harmonic; and of this science there are, 

35 as a fact, seven parts. Of these one and the first is to 
define the genera, and to show what are the permanent and 
what are the changeable elements presupposed by this 
distinction. None of our predecessors have drawn this dis¬ 
tinction at all; nor is this to be wondered at. For they 
confined their attention to the Enharmonic genus, to the 



neglect of the other two. Students of instruments, it is 
true, could not fail to distinguish each genus by ear, but 
none of them reflected even on the question, At what point 
does the Enharmonic begin to pass into the Chromatic ? 
For their ability to discriminate each genus extended not to 
all the shades, inasmuch as they were not acquainted with 
all styles of musical composition or trained to exercise a 
nice discrimination in such distinctions ; nor did they even 
observe that there were certain loci of the notes that alter 
their position with the change of genus. These reasons 
sufficiently explain why the genera have not as yet been 
definitely distinguished; but it is evident that we must 
supply this deficiency if we are to follow the differences 
that present themselves in works of musical composition. 

Such is the first branch of Harmonic. In the second we 
shall deal with intervals, omitting, to the best of our ability, 
none of the distinctions to be found in them. The majority 
of these, one might say, have as yet escaped observation. 
But we must bear in mind that wherever we come upon a 
distinction which has been overlooked, and not scientifically 
considered, we shall there fail to recognize the distinctions 36 
in works of melodic composition. 

Again, since intervals are not in themselves sufficient to 
distinguish notes—for every magnitude, without qualifica¬ 
tion, that an interval can possess is common to several 
musical functions—the third part of our science will deal 
with notes, their number, and the means of recognizing 
them; and will consider the question whether they are 
certain points of pitch, as is vulgarly supposed, or whether 
they are musical functions, and also what is the meaning of 
a musical ‘function.’ Not one of these questions is clearly 
conceived by students of the subject. 

The fourth part will consider scales, firstly as to their 
number and nature, secondly as to the manner of their 



construction from intervals and notes. Our predecessors 
have not regarded this part of the subject in either of these 
respects. On the one hand, no attention has been devoted 
to the questions whether intervals are collocated in any 
order to produce scales, or whether some collocations may 
not transgress a natural law. On the other hand, the dis¬ 
tinctions in scales have not been completely enumerated by 
any of them. As to the first point, our forerunners simply 
ignored the distinction between ‘ melodious ’ and ‘ un- 
melodious ’; as to the second, they either made no attempt 
at all at enumeration of scale-distinctions, confining their 
attention to the seven octave scales which they called 
Harmonies; or if they made the attempt, they fell very 
short of completeness, like the school of Pythagoras of 
37 Zacynthus, and Agenor of Mitylene. The order that dis¬ 
tinguishes the melodious from the unmelodious resembles 
that which we find in the collocation of letters in language. 
For it is not every collocation but only certain collocations 
of any given letters that will produce a syllable. 

The fifth part of our science deals with the keys in which 
the scales are placed for the purposes of melody. No explana¬ 
tion has yet been offered of the manner in which those keys 
are to be found, or of the principle by which one must be 
guided in enunciating their number. The account of the 
keys given by the Harmonists closely resembles the obser¬ 
vance of the days according to which, for example, the tenth 
day of the month at Corinth is the fifth at Athens, and the 
eighth somewhere else. Just in the same way, some of 
the Harmonists hold that the Hypodorian is the lowest 
of the keys; that half a tone above lies the Mixolydian; 
half a tone higher again the Dorian; a tone above the 
Dorian the Phrygian; likewise a tone above the Phrygian the 
Lydian. The number is sometimes increased by the addi¬ 
tion of the Hypophrygian clarinet at the bottom of the list. 



Others, again, having regard to the boring of finger-holes 
on the flutes, assume intervals of three quarter-tones between 
the three lowest keys, the Hypophrygian, the Hypodorian, 
and the Dorian; a tone between the Dorian and Phrygian; 
three quarter-tones again between the Phrygian and Lydian, 
and the same distance between the Lydian and Mixolydian. 
But they have not informed us on what principle they have 38 
persuaded themselves to this location of the keys. And 
that the close packing of small intervals is unmelodious and 
of no practical value whatsoever will be clear in the course 
of our discussion. 

Again, since some melodies are simple, and others contain 
a modulation, we must treat of modiilation, considering 
first the nature of modulation in the abstract, and how it 
arises, or in other words, to what modification in the melodic 
order it owes its existence; secondly, how many modulations 
there are in all, and at what intervals they occur. On these 
questions we find no statements by our predecessors with 
or without proof. 

The last section of our science is concerned with the 
actual construction of melody. For since in the same 
notes, indifferent in themselves, we have the choice of 
numerous melodic forms of every character, it is evident 
that here we have the practical question of the employment 
of the notes ; and this is what we mean by the construction 
of melody. The science of harmony having traversed the 
said sections will find its consummation here. 

It is plain that the apprehension of a melody consists in 
noting with both ear and intellect every distinction as it 
arises in the successive sounds—successive, for melody, 
like all branches of music, consists in a successive pro¬ 
duction. For the apprehension of music depends on these 
two faculties, sense-perception and memory; for we must 39 
perceive the sound that is present, and remember that which 



is past. In no other way can we follow the phenomena of 

Now some find the goal of the science called Harmonic 
in the notation of melodies, declaring this to be the ultimate 
limit of the apprehension of any given melody. Others 
again find it in the knowledge of clarinets, and in the ability 
to tell the manner of production of, and the agencies 
employed in, any piece rendered on the clarinet. 

Such views are conclusive evidence of an utter miscon¬ 
ception. So far is notation from being the perfection of 
Harmonic science that it is not even a part of it, any more 
than the marking of any particular metre is a part of 
metrical science. As in the latter case one might very well 
mark the scheme of the iambic metre without understanding 
its essence, so it is with melody also; if a man notes down 
the Phrygian scale it does not follow that he must know the 
essence of the Phrygian scale. Plainly then notation is not 
the ultimate limit of our science. 

That the premises of our argument are true, and that the 
faculty of musical notation argues nothing beyond a dis¬ 
cernment of the size of intervals, will be clear on considera¬ 
tion. In the use of signs for the intervals no peculiar 
mark is employed to denote all their individual distinctions, 
40 such as the several methods of dividing the Fourth, which 
depend on the differences of genera, or the several figures 
of the same interval which result from a variation in the 
disposition of the simple intervals. It is the same with 
the musical functions proper to the natures of the different 
tetrachords; the same notation is employed for the tetra- 
chords Hyperbolaeon, Neton, Meson, and Hypaton. Thus 
the signs fail to distinguish the functional differences, and 
consequently indicate the magnitudes of the intervals, and 
nothing more. But that the mere sense-discrimination of 
magnitudes is no part of the general comprehension of 



music was stated in the introduction, and the following 
considerations will make it patent. Mere knowledge of 
magnitudes does not enlighten one as to the functions of the 
tetrachords, or of the notes, or the differences of the genera 
or, briefly, the difference of simple and compound intervals, 
or the distinction between modulating and non-modulating 
scales, or the modes of melodic construction, or indeed 
anything else of the kind. 

Now if the Harmonists, as they are called, have in their 
ignorance seriously entertained this view, while there is 
nothing preposterous in their motives, their ignorance must 
be profound and invincible. But if, being aware that 
notation is not the final goal of Harmonic, they have pro¬ 
pounded this view merely through the desire to please 
amateurs, and to represent as the perfection of the science 
a certain visible activity, their motives deserve condemnation 41 
as very preposterous indeed. In the first place they would 
constitute the amateur judge of the sciences—and it is 
preposterous that the same person should be learner and 
judge of the same thing; in the second place, they reverse 
the proper order in their fancy of representing a visible 
activity as the consummation of intellectual apprehension; 
for, as a fact, the ultimate factor in every visible activity is 
the intellectual process. For this latter is the presiding and 
determining principle; and as for the hands, voice, mouth, 
or breath—it is an error to suppose that they are very much 
more than inanimate instruments. And if this intellectual 
activity is something hidden deep down in the soul, and is 
not palpable or apparent to the ordinary man, as the 
operations of the hand and the like are apparent, we must 
not on that account alter our views. We shall be sure to 
miss the truth unless we place the supreme and ultimate, not 
in the thing determined, but in the activity that determines. 

No less preposterous is the above-mentioned theory 

o 2 195 


concerning clarinets. Nay, rather there is no error so 
fatal and so preposterous as to base the natural laws of 
harmony on any instrument. The essence and order of 
harmony depend not upon any of the properties of instru¬ 
ments. It is not because the clarinet has finger-holes and 
42 bores, and the like, nor is it because it submits to certain 
operations of the hands and of the other parts naturally 
adapted to raise and lower the pitch, that the Fourth, and 
the Fifth, and the Octave are concords, or that each of the 
other intervals possesses its proper magnitude. For even 
with all these conditions present, players on the clarinet 
fail for the most part to attain the exact order of melody; 
and whatever small success attends them is due to the 
employment of agencies external to the instrument, as in 
the well-known expedients of drawing the two clarinets 
apart, and bringing them alongside, and of raising and 
lowering the pitch by changing the pressure of the breath. 
Plainly, then, one is as much justified in attributing their 
failures as their success to the essential nature of the 
clarinet. But this would not have been so if there was 
anything gained by basing harmony on the nature of an 
instrument. In that case, as an immediate consequence of 
tracing melody up to its original in the nature of the 
clarinet, we should have found it there fixed, unerring, and 
correct. But as a fact neither clarinets nor any other 
instrument will supply a foundation for the principles of 
harmony. There is a certain marvellous order which 
belongs to the nature of harmony in general; in this order 
every instrument, to the best of its ability, participates 
under the direction of that faculty of sense-perception on 
which they, as well as everything else in music, finally 
depend. To suppose, because one sees day by day the 
finger-holes the same and the strings at the same tension, 
that one will find in these harmony with its permanence 



and eternally immutable order—this is sheer folly. For 43 
as there is no harmony in the strings save that which the 
cunning of the hand confers upon them, so is there none in 
the finger-holes save what has been introduced by the same 
agency. That no instrument is self-tuned, and that the 
harmonizing of it is the prerogative of the sense-perception 
is obvious, and requires no proof. It is strange that the 
supporters of this absurd theory can cling' to it in face of the 
fact that clarinets are perpetually in a state of change; and 
of course what is played on the instrument varies with the 
variation in the agencies employed in its production. It is 
surely clear then that on no consideration can melody be 
based on clarinets; for, firstly, an instrument will not supply 
a foundation for the order of harmony, and secondly, even 
if it were supposed that harmony should be based on some 
instrument, the choice should not have fallen on the clarinet, 
an instrument especially liable to aberrations, resulting from 
the manufacture and manipulation of it, and from its own 
peculiar nature. 

This will suffice as an introductory account of Harmonic 
science; but as we prepare ourselves to enter upon the 
study of the Elements we must at the outset attend to the 
following considerations. Our exposition cannot be a suc¬ 
cessful one unless three conditions be fulfilled. Firstly, 
the phenomena themselves must be correctly observed; 
secondly, what is prior and what is derivative in them must 44 
be properly discriminated; thirdly, our conclusions and 
inferences must follow legitimately from the premises. And 
as in every science that consists of several propositions the 
proper course is to find certain principles from which to 
deduce the dependent truths, we must be guided in our 
selection of principles by two considerations. Firstly, every 
proposition that is to serve as a principle must be true and 

evident; secondly, it must be such as to be accepted by the 



sense-perception as one of the primary truths of Harmonic 
science. For what requires demonstration cannot stand as 
a fundamental principle ; and in general we must be watch¬ 
ful in determining our highest principles, lest on the one 
hand we let ourselves be dragged outside the proper track 
of our science by beginning with sound in general regarded 
as air-vibration, or on the other hand turn short of the flag 
and abandon much of what truly belongs to Harmonic. 

There are three genera of melodies; Diatonic, Chromatic, 
and Enharmonic. The differences between them will be 
stated hereafter; this we may lay down, that every melody 
must be Diatonic, or Chromatic, or Enharmonic, or blended 
of these kinds, or composed of what they have in common. 

The second classification of intervals is into concords 
and discords. The two most familiar distinctions in 
intervals are difference of magnitude, and difference between 
concords and discords; and the latter of these is embraced 
by the former, since every concord differs from every discord 
in magnitude. Now there being many distinctions among 
45 concords, let us first treat of the most familiar of them, 
namely, difference of magnitude. We assume then eight 
magnitudes of concords; the smallest, the Fourth—deter¬ 
mined as smallest by the abstract nature of melody; for 
while we can produce several smaller intervals, they are all 
discords ; the next smallest, the Fifth, all intervals between 
the Fourth and Fifth being discords; the third smallest, 
the sum of the first two, that is the Octave, all intervals 
between the Fifth and the Octave being discords. So far we 
have been stating what we have learned from our predeces¬ 
sors ; henceforth we must arrive at our conclusions unaided. 

In the first place then we shall assert that if any concord 
be added to the octave the sum is a concord. This property 
is peculiar to the octave. For if to an octave be added any 
concord, whether less than, equal to, or greater than itself, 


the sum is a concord. But this is not the case with the 
two smallest concords. For the doubling of a Fourth or 
Fifth does not produce a concord; nor does the addition 
to either one of them of the concord compounded of the 
octave and that one; but the sum of such concords will 
always be a discord. 

A tone is the excess of the Fifth over the Fourth; the 46 
Fourth consists of two tones and a half. The following 
fractions of a tone occur in melody: the half, called a semi¬ 
tone ; the third, called the smallest Chromatic diesis; the 
quarter, called the smallest Enharmonic diesis. No smaller 
interval than the last exists in melody. Here we have two 
cautions for our hearers; firstly, many have misunderstood 
us to say that melody admits the division of the tone into 
three or four equal parts. This misunderstanding is due to 
their not observing that to employ the third part of a tone 
is a very different thing from dividing a tone into three 
parts and singing all three. Secondly, from an abstract 
point of view, no doubt, we regard no interval as the small¬ 
est possible. 

The differences of the genera are found in such a tetra- 
chord as that from Mese to Hypate, where the extremes are 
fixed, while one or both of the means vary. As the variable 
note must move in a certain locus, we must ascertain the 
limits of the locus of each of these intermediate notes. The 
highest Lichanus is that which is a tone removed from the 
Mese. It constitutes the genus Diatonic. The lowest is 
that which is two tones below the Mese; this is Enharmonic. 
The locus of the Lichanus is thus seen to be a tone. 
The interval between the Parhypate and Hypate cannot, 
plainly, be less than an enharmonic diesis, for this latter is 47 
the minimum melodic distance. It is to be observed also 
that it can only be extended to twice that distance; for 

when the Lichanus in its descent, and the Parhypate in its 



ascent reach the same pitch, the locus of each note finds its 
limit. Thus it is seen that the locus of the Parhypate is not 
greater than the smallest diesis. 

This proposition has afforded some students great per¬ 
plexity. ‘ If,’ they ask in surprise, ‘ the interval between 
the Mese and the Lichanus (assuming it to be any one of 
the above-mentioned intervals) be increased or diminished, 
how can the note bounding the new interval be a Lichanus ? 
There is admittedly but one interval between the Mese and 
Paramese, and again between the Mese and Hypate, and in 
fact between any pair of the permanent notes. Why then 
should we admit a plurality of intervals between the Mese 
and the Lichanus ? Surely it would be better to change the 
names of the notes; and restricting the term Lichanus to 
any one of them, the two-tone or any other, to employ other 
designations for the rest. For notes that bound unequal 
magnitudes must be different notes. And one might add 
that the converse is equally valid, namely, that the bound¬ 
aries of equal magnitudes must have the same designations.’ 
To these objections the following reply was given. In the 
first place, to postulate that a difference in notes necessarily 
implies a difference in the magnitudes bounded by them is 
a startling innovation. We see that the Nete and Mese 
differ in function from the Paranete and Lichanus, and the 
Paranete and Lichanus again from the Trite and Parhypate, 
and these latter again from the Paramese and Hypate; and 
48 for this reason each pair has names of its own, though the 
contained interval is in every case a Fifth. Thus it is seen 
that a difference in the contained intervals is not necessarily 
implied by a difference of notes. 

That the converse implication is equally inadmissible will 
appear from the following remarks. In the first place, if 
we seek particular designations to suit every increase and 
decrease in the intervals of the Pycnum, we shall evidently 



need an infinite vocabulary, since the locus of the Lichanus 
is infinitely divisible. For as a matter of fact, to which of 49 - 7 
the disputants as to the shades of the genera should we give 
our adherence ? Every one is not guided by the same divi¬ 
sions in harmonizing the chromatic or enharmonic scale. 

Why then should the term Lichanus be applied to the two- 
tone Lichanus rather than to one slightly higher ? Which¬ 
ever division be employed, the ear equally recognizes an 
enharmonic genus; yet it is plain that the magnitudes of 
the intervals are different in the two divisions. In the 48. 15 
second place, if we have eyes exclusively for equality and 
inequality we shall miss the distinction between the like 
and unlike. Thus we shall have to restrict the term Pycnum 
to one particular magnitude; as likewise evidently the 
terms Enharmonic and Chromatic; for they too are deter¬ 
mined not to a point but to a locus. But it is evident that 
such a restriction is not in accordance with the mode in 
which sense forms its representations. It is by considering 
the common qualities found in some one class, not the 
magnitude of some one interval, that sense employs such 
terms as Pycnum, Chromatic, Enharmonic. That is to say, 
it constitutes a class Pycnum to embrace every case in 
which the two intervals occupy a, smaller space than the 
one; for in all Pycna, though they are unequal in size, there 
is evident to the ear the sound of a certain compression. 
Likewise it constitutes a class Chromatic to embrace all 
cases in which the Chromatic character is apparent. For 
the ear detects a motion peculiar to each of the genera, 
though each genus employs not one but many divisions of 49 
the tetrachord. Thus it is clear that, while the magnitudes 
change, the genus may remain unaltered, for up to a certain 
point changes in the magnitudes do not involve a change of 
genus. And if the genus remains the same, it is reasonable 
to suppose that the functions of the notes may be permanent 



also. For the species of the tetrachord is the same, and for 
this reason we must hold that the boundaries of the intervals 
are the same notes. In general, as long as the names of 
the extreme notes remain the same, the higher being called 
Mese, and the lower Hypate, so long will the names of the 
intermediate notes also remain the same, the higher being 
called Lichanus, and the lower Parhypate. For the notes 
between the Mese and Hypate are always stamped by the 
ear as Lichanus and Parhypate. To demand that all notes 
bounding equal intervals should have the same names, or 
that all notes bounding unequal intervals should have 
different names, is to join battle with the evidence of the 
senses. For in melody we make the interval between the 
Hypate and Parhypate sometimes equal and sometimes 
50 unequal to that between the Parhypate and Lichanus. 
Now in the case of two equal consecutive intervals it is 
impossible that the notes bounding each of them should be 
designated by the same terms, unless the middle note is to 
have two names. The absurdity is also evident when the 
above-mentioned intervals are unequal. For it is impossible 
that one of any pair of such names should change while the 
other remains the same; since the names have meaning 
only in their relation to one another. So much for this 

The term Pycnum we shall employ in all cases when, in 
a tetrachord whose extremes form a Fourth, the sum of 
two of the intervals occupies a lesser space than the third. 
There are certain divisions of the tetrachord which stand 
out from the rest as familiar, because the magnitudes of the 
intervals in them are familiar. Of these divisions, one is 
Enharmonic, in which the Pycnum is a semitone, and its 
complement two tones; three are Chromatic, namely, the 
Soft, the Hemiolic, and the Tonic Chromatic. The division 
of the Soft Chromatic is that in which the Pycnum consists 


of two of the smallest Chromatic dieses, while its com¬ 
plement is expressed in terms of two quanta, namely, a 
semitone taken thrice, and a Chromatic diesis taken once, 
so that the sum of it amounts to three semitones and the 
third of a tone. This is the smallest of the Chromatic 
Pycna and its Lichanus is the lowest in this genus. The 
division of the Hemiolic Chromatic is that in which the 51 
Pycnum is one and a half times the Enharmonic Pycnum, 
and each Diesis one and a half times an Enharmonic 
diesis. It is manifest that the Hemiolic Pycnum is greater 
than the Soft, since the former is less than a tone by an 
Enharmonic diesis, the latter by a Chromatic diesis. The 
division of the Tonic Chromatic is that in which the Pyc¬ 
num consists of two semitones, and its complement of a tone 
and a half. Up to this point both the inner notes vary; 
but now the Parhypate, having traversed the whole of its 
locus, remains at rest, while the Lichanus moves an enhar¬ 
monic diesis. Thus the interval between the Lichanus 
and Hypate becomes equal to that between the Lichanus 
and Mese, so that the Pycnum does not occur in this 
division as in the preceding. The disappearance of the 
Pycnum in the division of the tetrachord is coincident with 
the first appearance of the Diatonic genus. There are two 
divisions of the Diatonic genus, the Soft and the Sharp 
Diatonic. The division of the Soft Diatonic is that in 
which the interval between the Hypate and Parhypate is 
a semitone, that between the Parhypate and Lichanus three 
Enharmonic dieses, that between the Lichanus and Mese 
five dieses. The division of the Sharp Diatonic is that in 
which the interval between the Hypate and Parhypate is 
a semitone, while each of the remaining intervals is a tone. 
Thus, while we have six Lichani, as there are six divisions 52 
of the tetrachord, one enharmonic, three chromatic, and 
two diatonic, we have but four Parhypatae, that is, two 



less than the divisions of the tetrachord. For the semitone 
Parhypate is employed for both diatonic divisions, and for 
the Tonic Chromatic. Thus, of the four Parhypatae, one 
is peculiar to the Enharmonic genus, while the Diatonic 
and Chromatic between them employ three. Of the in¬ 
tervals in the tetrachord, that between the Hypate and 
Parhypate may be equal to that between the Parhypate 
and Lichanus, or less than it, but never greater. That it 
may be equal is evident from the Enharmonic and Chro¬ 
matic division of the tetrachord; that it may be less is 
evident from the Diatonic scales, and also may be ascer¬ 
tained in the Chromatic by taking a Parhypate of the Soft, 
and a Lichanus of the Tonic Chromatic; for such divisions 
of the Pycnum sound melodious. But to adopt the opposite 
order produces an unmelodious result; for instance, to take 
the semitone Parhypate, and the Lichanus of the Hemiolic 
Chromatic, or the Parhypate of the Hemiolic, and the 
Lichanus of the Soft Chromatic. Such divisions produce 
an inharmonious effect. On the other hand, the interval 
between the Parhypate and Lichanus may be equal to, 
greater than, or less than that between the Lichanus and 
Mese. It is equal in the Sharp Diatonic, less in all the 
other shades^ and greater when we employ as Lichanus 
the highest of the Diatonic Lichani, and as Parhypate any 
one lower than that of the semitone. 

We shall next proceed to explain, beginning with a general 
53 indication, the method by which we should expect to deter¬ 
mine the nature of continuity. To put it generally, in 
investigating continuity the laws of melody must be our 
guide, nor must we imitate those who shape their account 
of continuity with a view to the massing of small inter¬ 
vals. Such theorists plainly disregard the natural sequence 
of melody, as appears from the number of dieses that 

they place in succession; for the voice’s power of con- 


necting dieses stops short of three. Thus it appears that 
continuity must not be sought in the smallest intervals, nor 
in equal nor in unequal intervals; we must rather follow 
the guidance of natural laws. Now, though it were no 
easy matter at present to offer an accurate exposition of 
continuity before we have explained the collocation of inter¬ 
vals, yet the veriest novice can see from the following 
reasoning that there is such a thing as continuity. It will 
be admitted that there is no interval which can be divided 
ad infinitum in melody, and that the natural laws of melody 
assign a maximum number of fractions to every interval. 
Assuming that this will be, or rather must be, admitted, we 
necessarily infer that the notes containing fractions of the 
said number are consecutive. To this class belong the 
notes which, as a matter of fact, have been in use from 
the earliest times, as for instance the Nete, the Paranete, 
and those that follow them. 

Our next duty will be to determine the first and most 
indispensable condition of the melodious collocation of 
intervals. Whatever be the genus, from whatever note one 54 
starts, if the melody moves in continuous progression either 
upwards or downwards, the fourth note in order from any 
note must form with it the concord of the Fourth, or the 
fifth note in order from it the concord of the Fifth. Any 
note that answers neither of these tests must be regarded 
as out of tune in relation to those notes with which it 
fails to form the above-mentioned concords. It must be 
observed, however, that the above rule is not all-sufficient 
for the melodious construction of scales from intervals. 

It is quite possible that the notes of a scale might form 
the above-mentioned concords with one another, and yet 
that the scale might be unmelodiously constructed. But 
if this condition be not fulfilled, all else is useless. Let 

us assume this then as a fundamental principle, the vio- 



lation of which is destructive of harmony. A law, in some 
respects similar, holds with regard to the relative position 
of tetrachords. If any two tetrachords are to belong to 
the same scale, one or other of the following conditions 
must be fulfilled; either they must be in concord with 
each other, the notes of one forming some concord or 
other with the corresponding notes of the other, or they 
must both be in concord with a third tetrachord, with 
which they are alike continuous but in opposite directions. 
This, in itself, is not sufficient to constitute tetrachords of 
the same scale: certain other conditions must be satisfied, 
55 of which we shall speak hereafter. But the absence of the 
condition renders the rest useless. 

When we consider the magnitudes of intervals, we find 
that while the concords either have no locus of variation, 
and are definitely determined to one magnitude, or have 
an inappreciable locus, this definiteness is to be found in 
a much lesser degree in discords. For this reason, the 
ear is much more assured of the magnitudes of the con¬ 
cords than of the discords. It follows that the most 
accurate method of ascertaining a discord is by the principle 
of concordance. If then a certain note be given, and it 
be required to find a certain discord below it, such as the 
ditone (or any other that can be ascertained by the method 
of concordance), one should take the Fourth above the 
given note, then descend a Fifth, then ascend a Fourth 
again, and finally descend another Fifth. Thus, the interval 
of two tones below the given note will have been ascer¬ 
tained. If it be required to ascertain the discord in the 
other direction, the concords must be taken in the other 
direction. Also, if a discord be subtracted from a concord 
by the method of concordance, the remaining discord is 
thereby ascertained on the same principle. For, subtract 
the ditone from the Fourth on the principle of concordance, 


and it is evident that the notes bounding the excess of the 
latter over the former will have been found on the same 
principle. For the bounding notes of the Fourth are con- 56 
cords to begin with ; and from the higher of these a concord 
is taken, namely, the Fourth above; from the note thus 
found another, namely, the Fifth below; from this again 
a Fourth above, and finally from this a Fifth below; and 
the last concord alights on the higher of the notes bound¬ 
ing the excess of the Fourth over the Ditone. Thus it 
appears that if a discord be subtracted from a concord by 
the method of concordance the complement also will have 
been thereby ascertained on the same principle. 

The surest method of verifying our original assumption 
that the Fourth consists of two and a half tones is the 
following. Let us take such an interval, and let us find 
the discord of two tones above its lower note, and the same 
discord below its higher note. Evidently the complements 
will be equal, since they are remainders obtained by sub¬ 
tracting equals from equals. Next let us take the Fourth 
above the lower note of the higher ditone, and the Fourth 
below the higher note of the lower ditone. It will be seen 
that adjacent to each of the extreme notes of the scale 
thus obtained there will be two complements in juxta¬ 
position, which must be equal for the reasons already given. 
This construction completed, we must refer the extreme 
notes thus determined to the judgement of the ear. If they 
prove discordant, plainly the Fourth will not be composed 57 
of two and a half tones; ^^nd just as plainly it will be so 
composed, if they form a Fifth. For the lowest of the 
assumed notes is, by construction, a Fourth of the higher 
boundary of the lower ditone; and it has now turned out 
that the highest of the assumed notes forms with the lowest 
of them the concord of the Fifth. Now as the excess of 

the latter interval over the former ‘is a tone, and as it is 



here divided into two equal parts; and as each of these 
equal parts which is thus proved to be a semitone is at 
the same time the excess of the Fourth over a ditone, 
it follows that the Fourth is composed of five semitones. 
It will be readily seen that the extremes of our scale 
cannot form any concord except a Fifth. They cannot 
form a Fourth; for there is here, besides the original Fourth, 
an additional complement at each extremity. They cannot 
form an octave; for the sum of the complements is less 
than two tones, since the excess of the Fourth over the 
ditone is less than a tone (for it is universally admitted 
that the Fourth is greater than two tones and less than 
three); consequently, the whole of what is here added to 
the Fourth is less than a Fifth; plainly then their sum 
cannot be an octave. But if the concord formed by the 
58 extreme notes of our construction is greater than a Fourth, 
and less than an octave, it must be a Fifth; for this is 
the only concordant magnitude between the Fourth and 



Successive Tetrachords are either Conjunct or Disjunct. 

We shall employ the term conjunction when two succes- 58. 
sive tetrachords, similar in figure, have a common note; the 
term disjunction, when two successive tetrachords similar in 
figure are separated by the interval of a tone. That successive 
tetrachords must be related in either of these ways, is evident 
from our axioms. For a series, in which each note forms 
a Fourth with the fourth note in order from it, will constitute 
conjunct tetrachords; while disjunct tetrachords result, when 59 
each note forms a Fifth with the fifth from it. Now as all 
successions of notes must fulfil one or other of these con¬ 
ditions, so all successive similar tetrachords must be either 
conjunct or disjunct. 

Difficulties have been raised by some of my hearers on 
the question of succession. It has been asked. Firstly, 
what is succession in general ? Secondly, does it appear in 
one form only, or in several? Thirdly, are conjunct and 
disjunct tetrachords equally successive ? To these questions 
the following answers have been given. In general, scales 
are continuous, whose boundaries either are successive or 
coincide. There are two forms of succession in scales; in 
the one, the upper boundary of the lower scale coincides 
with the lower boundary of the upper scale; in the other, 
the lower boundary of the higher scale is in the line of 
succession with the higher boundary of the lower scale. In 
the first of these forms, the scales of the successive tetra¬ 
chords have a certain space in common, and are necessarily 

P 209 



similar in figure. In the other form, they are separated 
from one another, and the species of the tetrachords may 
be similar, only on condition, however, that the separating 
interval is one tone. Thus we are led to conclude that two 
similar tetrachords are successive, if they are either separated 
by a tone, or if their boundaries coincide. Consequently 
similar successive tetrachords are either conjunct or dis¬ 

We also assert that two successive tetrachords either 
6o must be separated by no tetrachord whatsoever, or must not 
be separated by a tetrachord dissimilar to themselves. 
Tetrachords similar in species cannot be separated by a 
dissimilar tetrachord, and dissimilar but successive tetra¬ 
chords cannot be separated by any tetrachord whatsoever. 
Hence we see that tetrachords similar in species can be 
arranged in succession in the two forms above mentioned. 

The interval contained by successive notes is simple. 

For if the containing notes are successive, no note is 
wanting; if none is wanting, none will intrude; if none 
intrudes, none will divide the interval. But that which 
excludes division excludes composition. For every com¬ 
posite is composed of certain parts into which it is divisible. 

The above proposition is often the object of perplexity 
on account of the ambiguous character of the intervallic 
magnitudes. ‘ How,’ it is asked in surprise, ‘ can the ditone 
possibly be simple, seeing that it can be divided into tones ? 
Or, how again is it possible for the tone to be simple seeing 
that it can be divided into two semitones ? ’ And the same 
point is raised about the semitone. 

This perplexity arises from the failure to observe that 
some intervallic magnitudes are common to simple and 
compound intervals. For this reason the simplicity of an 
interval is determined not by its magnitude, but the relations 
of the notes that bound it. The ditone is simple when 


bounded by the Mese and Lichanus; when bounded by the 
Mese and Parh)rpate, it is compound. This is why we 6i 
assert that simplicity does not depend on the sizes of the 
intervals, but on the containing notes. 

In variations of genus, it is only the parts of the Fourth that 
undergo change. 

All harmonious scales consisting of more than one tetra- 
chord were divided into conjunct and disjunct. But conjunct 
scales are composed of the simple parts of the Fourth alone, 
so that here at least it will be the parts of the Fourth alone 
that will undergo change. Again, disjunct scales comprise 
besides these parts of the Fourth a tone peculiar to disjunc¬ 
tion. If then it be proved that this particular tone does 
not alter with variation of genus, evidently the change can 
affect only the parts of the Fourth. Now the lower of the 
notes containing the tone is the higher of the notes con¬ 
taining the lower of the disjunct tetrachords; as such we 
have seen that it is immovable in the changes of the genera. 
Again, the higher of the notes bounding the tone is the 
lower of the notes bounding the higher of the disjunct 
tetrachords; it likewise, as we have seen, remains constant 
through change of genus. Since therefore, it appears that 
the notes containing the tone do not vary with a change of 
genus, the necessary conclusion is that it is only the parts 
of the Fourth that participate in that change. 

Every Genus comprises at most as many simple intervals 62 
as are contained in the Fifth. 

The scale of every genus, as we have already stated, takes 
the form of conjunction or disjunction. Now it has been 
shown that the conjunct scale consists merely of the parts 
of the Fourth, while the disjunct scale adds a single interval 
peculiar to itself, namely the tone. But the addition of 
this tone to the parts of the Fourth completes the interval 
of the Fifth. Since therefore it appears that no scale of any 


genus taken in the one shading is composed of more simple 
intervals than those in the Fifth, it follows that every genus 
comprises at most as many simple intervals as are contained 
in the Fifth. 

In this proposition the addition of the words ‘at the most’ 
sometimes proves a stumbling-block. ‘ Why not,’ it is asked, 

‘ show without qualification that each genus is composed of 
as many simple intervals as are contained in the Fifth?’ 
The answer to this is that in certain circumstances each of 
the genera will comprise fewer intervals than exist in the 
Fifth, but never will comprise more. This is the reason 
that we prove first that no genu^ can be constituted of more 
simple intervals than there are in the Fifth; that every 
genus will sometimes be composed of fewer, is shown in 
the sequel. 

63 A Pycnum cannot be followed by a Pycnuni or by part of 
a Pycnum. 

For the result of such a succession will be that neither 
the fourth notes in order from one another will form Fourths, 
nor the fifth notes in order from one another Fifths. But 
we have already seen that such an order of notes is un- 

The lower of the notes containing the ditone is the highest 
note of a Pycnum^ and the higher of the notes containing the 
ditone is the lowest note of a Pycnum. 

For as the Pycna in conjunct tetrachords form Fourths 
with one another, the ditone must lie between them; 
similarly since the ditones form Fourths with one another, 
the Pycnum must lie between them. It follows that the 
Pycnum and the ditone must succeed one another altern¬ 
ately. Therefore it is evident that of. the notes containing 
the ditone, the lower will be the highest note of the Pycnum 
below, and the higher will be the lowest note of the 
Pycnum above. 


The notes containing the tone are both the lowest notes of 
a Pycnum. 

For in disjunction the tone is placed between tetrachords 
the boundaries of which are the lowest notes of a Pycnum ; 
and it is by these notes that the tone is contained. For the 
lower of the notes containing the tone is the higher of those 
containing the lower tetrachord; and the higher of those 
containing the tone is the lower of those containing the 
higher tetrachord. Therefore it is evident that the notes 
containing the tone will be the lowest notes of a Pycnum. 

A succession of two Ditones is forbidden. 64 

Suppose such a succession; then the higher ditone will 
be followed by a Pycnum below, and the lower ditone will 
be followed by a Pycnum above, for we saw that the note 
that forms the upper boundary of the ditone is the lowest 
note of a Pycnum. The result will be a succession of two 
Pycna; and as this has been proved unmelodious, the suc¬ 
cession of two ditones must be equally so. 

In Enharmonic and Chromatic scales a succession of two 
tones is not allowed. Suppose such a succession, first in 
the ascending scale; now if the note that forms the upper 
boundary of the added tone is musically correct, it must 
form either a Fourth with the fourth note in order from it, 
or a Fifth with the fifth in order; if neither of these con¬ 
ditions is satisfied, it must be unmelodious. But that 
neither of them will be satisfied, is clear. For if it be 
Enharmonic, the Lichanus, which is the fourth note in 
order from the added note, will be four tones removed 
from it. If it be Chromatic, whether of the Soft or Hemi- 
olic colour, the Lichanus will be further removed than 
a Fifth; and if it be of the Tonic Chromatic, the Lichanus 
will form a Fifth with the added note. But this does not 
satisfy our law which demands that either the fourth note 
should form a Fourth, or the fifth a Fifth. Neither condition 



is here fulfilled. It follows that the note constituting the 
upper boundary of the added tone will be unmelodious. 

Again, if the second tone be added below it will render 

65 the genus Diatonic. Therefore it is evident that in the 
Enharmonic and Chromatic genera a succession of two 
tones is impossible. 

In the Diatonic genus three consecutive tones are permitted; 
but no more. For let the contrary be supposed; then the 
note bounding the fourth tone will not form a Fourth with 
the fourth note from it, nor a Fifth with the fifth. 

In the same genus a succession of two semitones is not 
allowed. For first suppose the second semitone to be 
added below the semitone already present. The result is 
that the note bounding the added semitone neither makes 
a Fourth with the fourth note from it, nor a Fifth with the 
fifth. The introduction, then, of the semitone here will be 
unmelodious. But if it be added above the semitone 
already present, the genus will be Chromatic. Thus it 
is clear that in a Diatonic scale the succession of two 
semitones is impossible. 

It has now been shown which of the simple intervals can 
be repeated in immediate succession, and how often they 
can be repeated; and which of them on the contrary it is 
absolutely impossible to repeat at all. We shall now speak 
of the collocation of unequal intervals. 

A ditone may be succeeded either above or below by a 
Pycnum. For it has been proved that in conjunct tetra- 
chords these intervals follow alternately. Therefore each 
can succeed the other either in an ascending or descending 

A ditone can be followed by a tone in the ascending scale 
only. For suppose such a succession in the descending 

66 order. The result will be that the highest and the lowest 
note of a Pycnum will fall on the same pitch. For we saw 



that the note that forms the lower boundary of the ditone 
was the highest note of a Pycnum, and that the note that 
forms the upper boundary of the tone was the lowest note 
of a Pycnum. But if these notes fall on the one pitch, 
it follows that there is a succession of two Pycna. As this 
latter succession is unmelodious, a tone immediately below 
a ditone must be equally so. 

A tone can be followed by a Pycnum in the descending order 
only. For suppose such a succession in the opposite order; 
the same impossibility will be found to result again. The 
highest and lowest note of a Pycnum will fall on the same 
pitch, and consequently there will be a succession of two 
Pycna. This latter being unmelodious, the position of the 
tone above the Pycnum must be equally so. 

In the Diatonic genus, a tone cannot be both preceded and 
succeeded by a semitone. For the consequence would be 
that neither the fourth notes in order from one another 
would form a Fourth, nor the fifth a Fifth. 

A pair of tones, or a group of three tones may be both 
preceded and succeeded by a semitone; for either the fourth 
notes from one another will form a Fourth, or the fifth 
a Fifth. 

From the ditone there are two possible progressions upwards, 
one only downwards. For it has been proved that the 
ditone can be followed in the ascending scale by either 
a Pycnum or a tone. But more progressions upwards from 
the said interval there cannot be. For the only other 
simple interval left is the ditone, and two consecutive 
ditones are forbidden. In the descending order there is 67 
but one progression from the ditone. For it has been 
proved that a ditone cannot lie next a ditone, and that 
a tone cannot succeed a ditone in the descending order. 
Consequently the progression to the Pycnum alone remains. 

It is clear then that from the ditone there are two possible 



progressions upwards, one to the tone, and one to the 
Pycnum; and one possible progression downwards, to the 

From the Pycnum^ on the contrary, there are two possible 
progressions downwards, and one upwards. For it has been 
proved that in the descending scale a Pycnum can be 
followed by a ditone, or a tone. A third progression there 
cannot be. For the only remaining simple interval is the 
Pycnum, and a succession of two Pycna is forbidden. It 
follows that there are only two possible progressions from 
a Pycnum downwards. Upwards there is but one, to the 
ditone. For a Pycnum cannot adjoin a Pycnum, nor can 
a tone succeed the Pycnum in the ascending scale; there¬ 
fore the ditone alone remains. It is evident then that 
from the Pycnum there are two possible progressions down¬ 
wards, one to the tone, and one to the ditone; and one 
possible progression upwards, to the ditone. 

From the tone there is but one progression in either direction: 
downwards to the ditone, upwards to the Pycnum. It has 
been shown that in the descending scale the tone cannot 
be followed by a tone or by a Pycnum. Therefore the 
ditone alone remains. And it has been shown that in 
the ascending scale the tone cannot be followed by a tone 
or a ditone. Therefore the Pycnum alone remains. It 
follows that from the tone there is but one possible pro- 
68 gression in either direction, downwards to the ditone, and 
upwards to the Pycnum. 

The same law can be applied to the Chromatic scales, 
except of course that one must substitute for the ditone the 
interval between the Mese and Lichanus, which varies, 
according to the particular shade, with the size of the 

The same law will also hold good of the Diatonic scales. 

From the tone common to the genera there is one possible 


progression in either direction; downwards to the interval 
between the Mese and Lichanus, whatever it may happen 
to be in any particular shade of the Diatonic scales; 
upwards to the interval between the Paramese and Trite. 

Some persons have been much perplexed by this pro¬ 
position. They are surprised that we do not arrive at 
quite a contrary conclusion; for they think that the pro¬ 
gressions in either direction from the tone are innumerable, 
since there are innumerable possible magnitudes of the 
interval between the Mese and Lichanus, and of the 
Pycnum as well. To this objection we offered the following 
answer. To begin with, the same observation might be 
made equally well in the other cases we have considered. 
Evidently one of the two descending progressions from the 
Pycnum admits of innumerable possible magnitudes; like¬ 
wise one of the two ascending progressions from the ditone. 
For such an interval as that between the Mese and Lichanus 
admits of innumerable magnitudes, and the same may be 
said of such an interval as the Pycnum. Nevertheless there 
are but two progressions from the Pycnum downwards, and 
two from the ditone upwards; and similarly one from the 
tone in either direction. For the progressions must be 69 
ascertained in accordance with one individual shade in one 
particular genus. In making any musical phenomenon the 
object of scientific knowledge, its definite side should be 
insisted on, its indefinite features left in the background. 
Now in respect of the sizes of intervals and the pitch of 
notes, the phenomena of melody are indefinite, while in 
respect of functions, common qualities, and orders of 
arrangement, they are definite and determined. To take 
the first example that occurs, the progressions downwards 
from the Pycnum are in function and character determined 
as two in number. The first proceeds by the tone and 
brings the scale into the disjunct class; the second pro- 



ceeding by the other interval (whatever its size may be) 
brings the scale into the conjunct class. Hence we see also 
that there is but one possible progression in either direction 
from the tone, and that both these progressions alike 
produce but one class of scale—the disjunct. But it is 
quite plain from these observations, and from the nature 
of the facts, that if one seek to discover the possible pro¬ 
gressions by considering not one shade of one genus at 
a time, but all shades and all genera together, one will 
come upon an infinity of them. 

In the Chromatic and Enharmonic scales every note partici¬ 
pates in the Pycnum. For every note in the said genera is 
the boundary either of a part of the Pycnum, or of the tone, 
or of an interval such as that between the Mese and Licha- 
70 nus. The case of notes that bound the parts of the Pycnum 
requires no proof; it is immediately evident that they partici¬ 
pate in the Pycnum. And we proved already that the notes 
containing the tone are both the lowest notes of a Pycnum; 
we showed also that the lower of the notes containing the 
remaining interval was the highest of a Pycnum, and the 
higher of them the lowest of a Pycnum. Now as these are 
the only simple intervals, and each of them is contained by 
notes both of which participate in the Pycnum, it follows 
that every note in the Chromatic and Enharmonic genus 
participates in the Pycnum. 

One will readily see that the positions of the notes situated 
in the Pycnum are three in number^ since, as we know, a 
Pycnum cannot be followed by another Pycnum or part of 
one. For it is evident in consequence of this latter law, 
that the number of the said notes is so limited. 

It is required to prove that from the lowest only of the notes 
in a Pycnum there are two possible progressions in either 
direction^ while from the others there is but one. It has 

already been proved that from the Pycnum there are two 


progressions downwards, one to the tone, and one to the 
ditone. But to prove that there are two progressions 
downwards from the Pycnum is the same as proving that 
there are two progressions downwards from the lowest of 
the notes situated in the Pycnum; for this note marks the 
limit of the Pycnum. Again, it was proved that from the 
ditone there are two progressions upwards. But to say 
that there are two progressions upwards from the ditone is 
the same as saying that there are two progressions upwards 
from the higher of the notes bounding the ditone. For 
this note marks the upper boundary of the ditone. But it 71 
is clear that the same note which forms the upper boundary 
of the ditone also forms the lower boundary of the Pycnum; 
being the lowest note of a Pycnum (for this too was proved). 
Hence it is evident that from this note there are two 
possible progressions in either direction. 

It is required to prove that from the highest note of a 
Pycnum there is but one progression in either direction. It 
was proved that from a Pycnum there is but one pro¬ 
gression upwards. But to say that there is one progression 
upwards from the Pycnum is (for the reason given in the 
former proposition) the same as saying that there is but 
one from the note limiting it. 

Again, it was proved that from the ditone there is but 
one progression downwards: but to say that there is but one 
progression downwards from the ditone is (for the reason 
given) the same as saying that there is but one from the 
note bounding it. But it is evident that the note which 
bounds the ditone below is at the same time the upper 
boundary of the Pycnum; being the highest note of a 
Pycnum. It is plain, then, that from the given note there 
is but one possible progression in either direction. 

It is required to prove^ that from the middle note of a 
Pycnum there is but one progression in either direction. Now 



since the given note must be adjoined by some one or 
other of the three simple intervals, and there lies already 
a diesis on each side of it, plainly it cannot be adjoined on 
either side by either a ditone or a tone. For suppose 
a ditone to adjoin it; then either the lowest or the highest 
note of a Pycnum will fall on the same pitch as the given 
note, which is the middle note of a Pycnum; consequently 
there will be a succession of three dieses, no matter on 
72 which side the ditone be located. Again, suppose a tone 
to adjoin the given note; we shall have the same result. 
The lowest note of a Pycnum will fall on the same pitch as 
the middle note of a Pycnum, so that we shall again have 
three dieses in succession. But this succession is unmelo- 
dious; therefore it follows that there is but one possible 
progression from the given note in either direction. 

It has now been shown that from the lowest of the notes 
of a Pycnum there are two possible progressions in either 
direction ; while from the others in either direction there is 
but one. 

It is required to prove that two notes that occupy dissimilar 
positions in the Pycnum cannot fall on the same pitch without 
violating the nature of melody. Suppose, firstly, that the 
highest and lowest note of a Pycnum fall on the same pitch. 
The result will be two consecutive Pycna, and as this is 
unmelodious, it must be equally unmelodious that notes dis¬ 
similar in the Pycnum in the manner of the assumed notes 
should fall upon the same pitch. 

Again, it is evident that the notes also that are dissimilar 
in the other possible manner cannot have a common pitch. 
For if the highest or lowest note of a Pycnum coincide in 
pitch with a middle note, there necessarily results a succes¬ 
sion of three dieses. 

It is required to prove that the Diatonic genus is composed 

of two or of three or of four simple quanta. It has been 


already shown that each genus comprises at most as many 
simple intervals as there are in the Fifth. These are four 73 
in number. If then three of those four become equal, 
leaving but one odd,—as happens in the Sharp Diatonic— 
there will be only two different quanta in the Diatonic 
scale. Again, if two become equal and two remain unequal, 
which will result from the lowering of the Parhypate, there 
will be three quanta constituting the Diatonic scale, namely, 
an interval less than a semitone, a tone, and an interval 
greater than a tone. Again, if all the parts of the Fifth 
become unequal, there will be four quanta comprised in the 
genus in question. 

It is clear then that the Diatonic genus is composed of 
two or of three or of four simple quanta. 

It is required to prove that the Chromatic and Enharmonic 
genera are composed of three or four simple quanta. The 
simple intervals of the Fifth being four in number, if the 
parts of the Pycnum are equal, the genera in question will . 
comprise those quanta, namely, the half of the Pycnum, 
whatever its size may be, the tone, and an interval such as 
that between the Mese and Lichanus. If on the other 
hand the parts of the Pycnum are unequal, the said 
genera will be composed of four quanta, the least, an 
interval such as that between the Hypate and Parhypate, 
the next smallest one such as that between the Parhy¬ 
pate and Lichanus, the third smallest a tone, and the 
largest an interval such as that between the Mese and 

On this point the difficulty has been raised. How is it 
that all the genera cannot be composed of two simple 74 
quanta, as is the case with the Diatonic? We can now 
see the complete and obvious explanation of the difference. 
Three equal simple intervals cannot occur in succession 
in the Enharmonic and Chromatic genera; in the Diatonic 



they can. That is the reason that the last-named genus is 
sometimes composed of only two simple quanta. 

Passing from this subject we shall proceed to consider 
the meaning and nature of difference of species. We shall 
use the terms ‘ species ’ and ‘ figure ’ indifferently, applying 
both to the same phenomenon. Such a difference arises 
when the order of the simple parts of a certain whole is 
altered, while both the number and magnitude of those 
parts remain the same. Proceeding from this definition we 
have to show that there are three species of the Fourth. 
Firstly, there is that in which the Pycnum lies at the 
bottom; secondly, that in which a diesis lies on each side 
of the ditone; thirdly, that in which the Pycnum is above 
the ditone. It will be readily seen that there are no other 
possible relative positions of the parts of the Fourth. 



[The references in these notes are to the pages and lines of 
the present edition.] 

Page 95 , line 3. The term fieXos signifies a song, and as such 
includes the words, the melody proper, i. e. the alternation of 
higher and lower pitch, and the rhythm. But as the second 
of these factors is evidently that which is characteristic of song, 
it came to appropriate to itself the term /xeXo?. Then riXeiov 
fiiXos was used in the wider sense. Cp. Anonymus, § 29, TiXeiov 
Se fiiXos €o*rl ro (TvyKeifievov €K T€ Kal fjifXovs Kal pvdfiov. 

See also Aristides Quintilianus (ed. Meibom, p. 6, line 18). piXos 
then in the narrower sense signifies in Aristoxenus that moment 
of music which consists in the employment of higher and lower 
notes, always with the implication that the complete series of 
compossible higher and lower notes is determined by a natural 
law. This quality of peXos by which it is obedient to a law, or 
rather the embodiment of a law, is called ro fjppoapcpop: and 
consequently all true melody is an fjppocrpcpop peXos. Thus for 
the Greeks Harmony is the law of Melody, rj povaiKfj on the 
other hand is a term of very wide signification. Aristides Quin¬ 
tilianus (ed. Meibom, pp. 7, 8) gives the following analysis of it— 


. i ! ^ ^ ; rT~i 

pLepr) TevpiKo, P'^Pl f^uyy^Xri/cd 

1_ I _L_ 

I , J , I , 

perpiKov TTOiTjcris vnoKpiriKOP 


d-ppoPiKOP peXoTTOita opyapiKOP 

Now in which sense is the term pfXovs used in the passage 



before us? Marquard supposes in the general sense of the 
object-matter of fiovaiKrj. (In support of this view he might 
have quoted Anonymus, § 29, MovcriKfj iarip inKrTfjfirj decoprjTiKrj 
Kai irpaKTiK^ pfKovs TcXeiov re Kal opyaviKov.) But this is not in 
accordance with Aristoxenus’ use, and probably Westphal is 
right in interpreting it in its close and strict meaning. If so, 
what are the other sciences of it besides dppopiKfj ? Westphal 
replies, peXonoua, opyapiKrjy (cSiKrj (i.e. the sciences of composition, 
of instrumental music, of singing). 

1. 4 . piap Tipa avTci>p viroXa^elp Set k.t.X. — The construction of 
this sentence is Set vnoXa^eiP rrjp dppopiKrjp KaXovpeprjp npaypareiap 
€ipai piap TiPCL avTcbp (i. e. tS>p iSewj/), t€ rd^ei TrponTrjp ovcrapy k.t.X. 

Marquard and Westphal construe Sei vTroXa/Beip piap tip a 
avTcbPj Trjp dppopiicrjp KaXovpeprjPy eipai np ay pare lap tc rd^ei TTpiar-qp 
ovaaPy K.T.X., and translate ^we must regard one of them, namely 
Harmonic, as primary.’ But the Greek for ^ to be a good man ’ 
is not upai dpfjp dyaOos &p, 

rfjp dppopiKrjp. The English word ‘Harmony’ in no wise 
corresponds to the Greek dppovia. This latter properly signi¬ 
fies an adjustment or fitting together of parts. Hence, by 
being transferred from the method to the concrete object which 
embodies it, it is used to connote (a) a scale or system as 
a whole whose parts have been adjusted in their proper rela¬ 
tions, (d) the enharmonic scale, because in that genus three notes 
of the Tetrachord are fitted most closely to one another, that is, 
placed at the smallest possible intervals. The term dppopiKrj 
signifies then the science of scales, that is the science by which 
we constitute a system of related and compossible notes. 
Harmony in the modern sense of the word was in its infancy 
among the ancient Greeks. 

1. 6. Tvyxdp€i yap ovaa rSap Trp&Toup d€G)prjTiKr}* ravra S’ co'tlp 
oaa. The MSS reading is here plainly ungrammatical. If we 
retain TTpoarri to>p 6€(oprjTiK&Py we must change ravra to ravrrjSy ‘ to 
this science belong/ &c. [cp. 1 . 12, ovkcti ravrrjs cVtiV]. But 
I prefer to read as above with Westphal, in which case of course 
ravra refers to rd 7rpa>ra. Cp. Anonymus (a mere echo of 
Aristoxenus), § 31? 7rp(0r€V0P Se p^pos rrjs povaiKrjs fj dppopiKrj iarC 
rd ydp ip povaiKfj 7rpa>Ta avrrj dccopei. Also § 19, reap Sc r^s 


fiovcriKrj^ fi€pS)V Kvpi&Tarov iari koI np^rov to &ppoviK 6 v* tS)v yap 
rrpwTCOv povaiKrjs necfiVKc OcoDprjriKrj, Cp. also 1 . 1 4 of this page, 81 
hv Trdvra deo^peirai rd /card povaiKrjv, 

For the relation between Harmonic and Music, cp. Plutarch 
iie Musica^ 1142 F, (l>ap€pov 6* ap yepoiroj €i ns €Kd<rTrjp c^crafoiTO 
Ta>p € 7 na‘TTjpS)Vy rivos iarX Seaypr^TiKrj* 8 j]\op ydp on 17 pev dppopiKff 
y€vSiv T€ Toav tov fjppoapevov Kai 8ia(TTr]pjdT(dv KaX <rvaTrjpdToi>p KaX 
(fidoyyGyp koX topcdp koX /xcrajSoXwj/ crvarrjpanK^P icrn ypaxrnKrj* nop^ 
pa)T€pG) S* ovKCTi TavTrj TrpoeXOelp olop T€, &(rT oiSc C^reip Trapd 
TavTrjs TO 8iayva>vai 8vva(Tdaij noTepov otKeicos €Tkrj<f)€P 6 ttoitjt^s . . . 
TOP 'YTToScbpioj/ Topop iwX ttjp dp)(^p rj top Mi^oXiSiop T€ koX Adyptop 
€7rX Trjp €K^a(riP rj top *Y7ro(l>p{ryi6p re KaX ^piryiop eirX ttjp pecrrjp. 

1 . 16. The point of the passage lies in the possible ambiguity 
of the term dppopiKosy which properly signifying ‘concerned 
with scales ’ [cp. dppopiKfj = science of scales] might also mean 
‘ concerned with the enharmonic scale.’ Cp. note on 1 . 4. 

P. 96 , 1 . 2. Kai rot ra 8iaypdppaTd y’ avrSiP. See end of note 

on p. loi, 1 . I. 

1 . 4. nepX 8e Ta>p aXXcop p^yedcop re KaX o’XW^'^^p* ^ have 

changed the MSS reading yepSiP to peyeO^p for three reasons: 
(i) quite sufficient stress has been laid on the early theorists’ 
omission of the Chromatic and Diatonic genera, and further refer¬ 
ence to it is not required; (2) a reference to their omission of 
‘ other magnitudes ’ is required in view of what follows (cp. 1. 7); 
(3) the close connexion of yepcbp and axripArrop by re Kai would 
make it necessary to supply the qualification ip air<» re r© yepei 
TovT(p KaX Tols XoiTTois with both, which is obviously impossible. 

(Tx^puy which we shall translate by ‘Figure,’ signifies the 
arrangement or order of the parts of a whole, and two things 
differ in (rxwa if they have the same parts, but these parts are 
arranged in a different order. Thus the scale from C to ^ and 
the scale from -ff to ^ on the white notes of the piano are 
composed of the same intervals, five tones and two semitones, 
but they differ in a-x^pa or the arrangement of those intervals. 

1 . 6. dnoTeppopepoi ... to 8id iraaSip. By the phrase ro TpiTOP 
pepos Trjs oXt]s peX(D8ias is meant the Enharmonic genus, just as 
a few lines above tt^p nciaap ttjs peX<o8ias Td^ip means the Enhar¬ 
monic, Chromatic, and Diatonic Genera. 





Hence the MSS reading ev n yepos fxiyedos 8c is untenable. 

What is the rpirov pepog of /LteXwS/a from which the Harmonists 

can be said to have selected one genus ? According to Mar- 

quard dppLovia (in the sense of ‘melodic element in music’). 

But even granting that pL€\<o8ia here means music in general, 

and that music in general may be divided into dppopia, pvOpLos^ 

and Xdyoff, could this division have been so universally familiar 

that Aristoxenus would presuppose it, and employ the phrase 


TpiTov pipos without explanation ? 

I omit yei/off and Sc. The former might easily be inserted by 
an ignorant scribe, who not understanding rod rpirov pepovs 
missed the necessary reference to the enharmonic genus. The 
intrusion of ycVo? naturally entailed the addition of Sc. 

1 . II. An unknown polemic. 

1 . l8. (fycjpfjs. The term (jxoprj in Aristoxenus comprehends 
the human voice, and the sounds of instruments. See Ari¬ 
stotle, de Anhna^ 420 f) Sc (fxovrj yj/'ocftos rk iarip ip^v^ov* rSiv 
yap dyjrv^cop ov0€P (fxopeij dXXa KaO^ opoiorrjra Xcycrai (fx^peiv^ olov 

avXos Kal \vpa Koi Sera dXXa rcbv arj/v^ajp aTroracrip e^ei Kai pfKos Ka\ 


P. 97 , 1 . 2. I read cVi/LtcXcy for impeXebs of the MSS which 
(i) gives a weak construction to ycycViyrm, and (2) requires, as 
Marquard saw, the diopiaOcpros of 1 . 4 to be supplemented by 
an adverb. 

1 . 6. Ado-off. Lasus of Hermione, the well-known dithy- 
rambic poet, and teacher of Pindar. Suidas credits him with 
the authorship of the earliest work on the theory of Music. 
See Suidas s. v .; Athenaeus x, 455 c and xiv, 624 c; Herodotus 
vii. 6 ; Plutarch, de Musica^ 1141 B-C. 

’ETTiyoi/ciW. Disciples of Epigonus of Ambracia, a famous 
musical performer. See Athenaeus iv, 183 d and xiv, 637 f. 

1 . 7. TrXdroff. The spatial' image, under which Aristoxenus 
represents the pitch relations of notes, is that of an indefinite 

line x-y 

a b c 


on which the several notes appear as points abed [cp. Nico- 
machus (ed. Meibom, p. 24, 1 . 21), (l>06yyos iari (fxapq aro/Ltos*, olop 


fiovas Kar aKor]v\y and the intervals as the one-dimension spaces 
between them. The obvious objection to this conception is 
that it attributes quantity and so reality to the spaces between 
the notes, while it denies it to the notes themselves, whereas 
our senses tell us that the notes are the realities, and the 
intervals only their relations. This objection lies at the basis 
of the contending theory, here quoted by Aristoxenus, which 
assigns to notes a certain quantity or ^ breadth.’ 

1 . 16 . fi nfj fi€v TTfi S’ oS. For Aristoxenus’ answer to the 
question see p. 107,11. 13-19. 

1 . 17. I conjecture \€kt€ov for dUaiov of the MSS. Cf. note 
on p. 143,1. 13. 

1 .19. Probably Marquard’s SieX^oin-a is correct. duXopra is 
not objectionable in itself (cp. p. 98,1. 5, p. 108,1. 18, &c.); but 
if we retain it, the passage lacks any reference to the general 
treatment of the scale. 

1 . 22. nXeiovs elcrl (f>v(r€is fxeXovs. See p. IIO. 

P. 98 , 1 . 9. The meaningless avrrjs of the MSS may have 
been interpolated to produce a show of connexion between this 
paragraph and the preceding. 

1 . 17 * ols afia . . . (Tv/xjSatm. 


The distance between e and regarded as a whole, is an 
interval; regarded as a series of smaller distances, between e and 
/,/and gy g and it is a scale. 

1 . 21. Of Eratocles nothing is known beyond what we learn 
from Aristoxenus himself. 

1 . 22. on dno . . . fxiXos. That is, one has a choice between 
conjunction and disjunction. 







At the point 

the ascending melodic progression 

Q 2 



diverges into 

Similarly at 

branches into 



the descending melodic progression 


1 . 23. el dno navTos . . . yiyverai. Evidently the law only 
holds of those Fourths of which the boundaries are fixed notes. 

If we take the Fourth 

there is but one 

method of completing the melodic progression in each direction; 

- —— 

- 1 - 





^ _£_ 


^ _ 

P. 99 , 1 . 12. For the Perfect System or Scale see Introduction 
A § 29. 

1. 14. Kara (rvvBeaiVj ^ in respect of the method of their com¬ 
position,’ according as that may be by conjunction, disjunction, 
or a combination of both these methods. See Introduction A 

1 . 15* xara crx^H^ci. Cp. note on p. 96, 1 . 4* 

H probably supplies the true reading here. Marquard inserts 
Kal Kara Becriv on account of fifjTe Oeais in 1 . 17. But the latter 
words (which do not appear in H) are probably a dittograph to 
firjre (TvvOecris. Though decrts does not occur as a technical term 
in Aristoxenus, it might conceivably mean ^ key ’ on the analogy 
of Tideadai (see e. g. p. 128, 1. 7); but key-distinctions belong to 
a later part of the subject (p. 100, 11. 14-20) and are out of 
place here, Aristoxenus being well aware that such distinctions 
are not essentially scale-distinctions (see p. 100, 1. 16). 

1 . 25. ai/anoSeiKTois • .. yiyveaOai SeiKwrai, Eratocles, accord¬ 
ing to the criticism of Aristoxenus, would seem to have presup¬ 
posed the constitution of the octave scale 

and to have arrived at the enumeration of its Figures by showing 


that after proceeding through the various arrangements to be 
obtained by beginning successively with f gy Uj by Cy dy one is 
brought back again to the first Figure with which one started. 
Against this superficial empiricism Aristoxenus very justly 
urges that the Figures of the Fourth and Fifth and the laws of 
their collocation must be demonstrated prior to the enumeration 
of the Figures of the Octave. Otherwise we are not justified in 
limiting these Figures to seven. Why, for example, should we 
not admit the Figure 

Here we have a scale that is illegitimate though it consists of 
five tones and two semitones, because it violates the law of the 
Figures of the Fourth and Fifth and their collocation. 

P. 100, 1. lo. Several words must have been lost here 
the substance of which I have supplied. Aristoxenus is evi¬ 
dently insisting that the enumeration of the scales cannot be 
complete unless account be taken of the scales of mixed 
genus: therefore after the number of possible scales in each 
genus has been ascertained, we must, he tells us, mix genera 
and repeat the process of enumeration. But what is the sense 
of giving as a reason fpr the necessity of this process the fact 
that ‘ they,’ whoever ‘ they ’ may be, ‘ had not even perceived 
what mixture is ’ ? 

1 . 17. Marquard inserts tov tottov before airov and translates 
* though the space is in itself homogeneous.’ Westph^ rightly 
reads with the MSS and understands airov as equal to rod 

1 . 22. The question here raised is one of great importance. 
Are there any affinities between scales and keys ? By scales we 
mean so many series of notes in which abstraction is made of 
pitch and regard is had solely to the order of intervals. By 
keys we mean so many series of notes, in which the intervals 
and their order are identical, while each series is situated at 
a different pitch from every other. 

See Introduction A, § 22. 

P. 101 , 1 . I. Aristoxenus here contrasts two principles by 



which one might be guided in determining the relative positions 
of the keys proper to the several scales. One is the false 
principle of KarajrvKi^oixnsj or ‘ close-packing * of intervals; the 
other the true principle of the possibility of intermodulation. 
To understand the difference between these principles let us 
take the seven modes or scales of Table 20 in Introduction A, 
in the Enharmonic forms as follows: 









T.::-"- 77 .4. --J:,—a 


ym — 



I u ^ - 

1 a. I 



^ ^ 


Tonic , , , 

t 7 











and let us place all the notes supplied by these scales between 


in one series as follows: 

~ J— — 7r \ '~ " J 

rw ..TiF. :z,. 



Now we see that in this series there is no 

, no 



that is, 



there are several intervals of a semitone which are not 
divided into their apparently possible quarter-tones. At the 
same time it is evident that the tonics of these keys are so 
related to one another that it will be possible to pass directly or 
indirectly from any one to any other. (See note on p. 129, 1 .4.) 

Once more let us again take the same seven enharmonic 
modes, but changing the keys let us arrange them as follows : 











I I 





Writing in one series all the notes of these keys between 


we obtain the following result: 

Here we have an unbroken series of the absolutely smallest 
intervals (i.e. quarter-tones); but the keys are so related to one 
another, their tonics being spaced by the interval of three 



quarter-tones, that a modulation from one to another of them is 
impossible. (See note on p. 129, 1 . 4.) 

The first of the above sets of scales is arranged on the 
principle of possible intermodulation; the second on the prin¬ 
ciple of KaTanvKvcoais, or arrangement at the closest possible 
intervals. It is obvious that the former is the true principle of 
music. The unbroken series of small intervals may satisfy 
the eye, but to use the words of Aristoxenus [p. 129, 1 . i] it is 
eKfjLeXfjs Koi navra rponov axprjcrTosj that is, at variance with the 
nature of melody which forbids a succession of more than two 
quarter-tones; and of no practical value, because the only 
object in a relative determination of keys is to render inter¬ 
modulation possible. 

We can now understand the statement of Aristoxenus [p. 96, 
1. 2] that the tables of the early harmonists, though only con¬ 
structed with a view to the Enharmonic Genus, exhibited the 
whole melodic system. In such a series as that last given all 
the chromatic and diatonic scales are implicitly presented. [It 
is however possible that cfijJXou in this passage may signify 
‘ professed to exhibit.’] 

1 . 2. I read tlvcov for MSS 

1 . 3. TTcpl TovTov . . . TOV0* fjpuv. I havo coiTected the read¬ 
ings of the MSS by inserting on before cVl ^paxv> Then on 
eviois avp^e^rjKep irepl tovtov tov plpovs etprjKevaij ovd^vl Se crv/x- 
KadoXov elprjKevai is the subject of (I)ap€p6v y€y€prjTaL, 

1 . 7. TremyrjTai of Me. for 7r€7rolrjTai is an interesting example 
of a mistake arising from dictation. Such mistakes are frequent 
in the MSS of Aristoxenus. Compare p. 144, 1 . 12 17 tovtois 
(T vp^xrji for oi TovTOLs crvpex^^Sj p. 139? 1 . 18 b^iKPoaip (in R) for 
bq KLpqaLPj p. 139, 1 . 13 610*11' G)s (in R) for els epos^ p. I 37 > 1 . 15 
VTTapvTTarq (in B) for q TrapvnaTq ; also such spellings as dneTovPj 

aX\)(£KTLP^ TTlKPOy CipciO-^O), for CLTTaLTOVP^ dXXoLCOaiPj TTVKpdj 

axpqcTTay eipfjaffo), and the constant confusion of subjunctive and 
indicative forms. 

P. 102 , 1 . 8. TTorepop ,. .€ot 1 o’Keylrecos. See Introduction B § 2. 
Aristoxenus is not concerned with the truth or falsity of the 
physical theory of sound. 

1 . II. TO be Kiprjaai tovtcop eKarepop. The true reading here 


is hard to conjecture. Marquard’s first idea was to omit 
Sc and understand KLvrjaai in the sense of ‘ to raise or moot a 
question ’; but he afterwards abandoned this view on the ground 
that KLP€LP occurring so often in the same passage in the technical 
sense of ‘motion’ could not in this one case bear a different 
meaning. [On this point Mr. Goligher aptly cites Berkeley’s 
Principles of Human Knowledge^ § 77 •* ‘ If what you mean by 
the word matter be only the unknown support of unknown 
qualities, it is no matter whether there is such a thing or no, 
since it in no way concerns us.’] His final conjecture is Sta- 
Kpivai for Sc Kivrjcrai^ and he gives as the meaning of the passage 
‘ for the purposes of the present argument it is not necessary 
to decide this question.’ But this is, I think, quite untenable. 
Even if we grant that ‘ it is not necessary to discriminate each 
of these things ’ is a possible expression of the meaning ‘ it is 
not necessary to decide for either of these alternatives,’ yet it 
is clear from 1. 7 that eKarepov tovtcop must here mean ‘ each of 
these phenomena,’ namely, the two kinds of voice-motion. Once 
we admit this, we must reject to biaKplvai ; for it is obviously 
false to say that ‘ the discrimination of these phenomena from 
one another is unnecessary for our argument.’ 

I believe the true reading to be roO SievKpLprjaaL (or some such 
word) TovTcov eKarcpoVy where roG SuvKpiprja-ai is the genitive of 
the material after rfjp epeaToxrap TTpaypar^iav: and the meaning 
to be ‘ the question of the objective possibility of rest and motion 
of the voice belongs to a different sphere of speculation, and 
is irrelevant to our present purpose, which is to discriminate 
each of these two phenomena from the other.’ 

1 . 26. bia Trd^off. As in the case of impassioned recitation. 
Cp. Aristides Quintilianus (ed. Meibom, p. 7, 1 . 23), 17 ph ovv aw 
€Xr}£ (KLprjais) iariVy fj SiaXc-yd/xc^a* pearj Sc, ^ raff t&v TToirjpaTcop 
dvaypaxrei^ 7roiovpje0a* SLaarrjpaTLKrj Sc fj Kara piaov tS>v dirkSiv 
<l)oi)vd>p TToaa TTOLOvpevrj SiaaTrjpaTa Ka\ povdsj rj riff koX peXaSiKfj 

P. 103 , 11 . 1-6. As the monotone of declamation is a license 
of speech, so is the tremolo a license of music; and the use of 
either, if not justified by the presence of an exceptional emotion, 
is a sin against nature. 



1 . 3. Probably oa(o yap av , , , Troir](T(op€Vy the reading of B and 
R, is right. 

I. 16. emraaLS and aveais signify the processes^ not the statesy 
of tension and relaxation. Though properly applying only to 
strings, they are used metaphorically of the human voice and 
the sounds of wind-instruments. 

P. 104 , 1 . 14. €7ri Tov ivavTiov tottoj/, the reading of B, is un¬ 
doubtedly right. Cp. p. 145, 1 . 9; also the phrases iirl to 

CTTl TO ^apv. 

1 . 20. TpiTov. WestphaFs conjecture of nipTrrov is, I think, 
unnecessary, in spite of p. 106, 1 . 9. For the purposes of the 
argument imraais and may be regarded as subdivisions 

of one conception, and similarly o^vrrjs and fiapvTrjs. 

1 . 23. pfj TapaTT€Ta>a‘av k.t.X. Aristoxenus very rightly in¬ 
sists that the validity of his distinction is not injured by the 
fact that it is verbally incompatible with the theory of the 
Physicists. When he speaks of motion and rest of the voice, 
he refers to certain phenomena which tAe ear distinguishes as 
motion and rest, though this distinction may directly contradict 
the ultimate nature of these phenomena as apprehended by the 
intellect. Thus, when the Physicist presses upon him the 
theory that all sound is vibration or motion, and urges that 
motion at rest is a contradiction, he replies : ‘ According to the 
evidence of the ear (which, for my purposes, is the final test 
of truth) the voice is at rest in cases where, according to your 
theory of objective facts, the rate of its vibration is constant; 
consequently, to distinguish the phenomena before us, we may 
employ the language of the ear just as well as the language of 

P. 105 , 1 .15. The MSS read here o fjpels Xiyopev Kiurjaiv re 
Ka\ rjpepiap (fxovrjs Kol b eK^lvoi kIvtjo'lv which is translated ‘it is 
fairly evident what we mean by rest and motion of the voice, 
and what they mean by motion.’ But this is unsatisfactory, not 
only on account of the weakness of the conclusion thus drawn, 
but also because 5 5 ’... Kivr]cnv being a relative sentence and 
not an indirect question, the correct translation would be ‘ the 
thing to which we give the name of rest and motion of the 
voice is a fairly patent thing, as is also the thing to which 


they give the name of motion,’ which does not give the required 

P. 107 j 1 . 3. SicVccaff eKaxLOTrjs. That is a quarter-tone. 
Aristoxenus uses SiWiy for any interval less than a semitone. 

1 . 5 « i^a\ ^vvUvai k.t.X. Aristoxenus does not mean that 
we cannot hear any interval smaller than a quarter-tone, but 
that though we may be conscious of such a smaller interval, 
we can have no perception of it as a musical entity, since we 
cannot estimate its magnitude in reference to other musical 

P. 108 , 1 . 21. Kaff fjv TCL (rvficfxova Tcbv The only con¬ 

cords recognized by Greek theorists are the Fourth; the Fifth ; 
the Octave ; the sum of two or more Octaves : the sum of one 
or more Octaves and a Fourth ; the sum of one or more Octaves 
and a Fifth. 

In his note on this passage Marquard has collected several 
definitions of concords and discords. 

According to Gaudentius [ed. Meibom, p. ii, 1 . 17] avfKfxopoL 

&€ !l)V aim Kpovofieva>p rj av\ovii€PG)p del to fieXos tov ^apvrepov Trpos 
TO d^v Kal TOV o^vTcpov npos to ^apv to avTo ^ ... Sidcfxovoi Sc (Sp apui 
KpovopipQDP rj avXoviiivoDV ovdip ti (l)aip€Tai tov pLcXovs eipai tov 
0apvT€pov npos to o^v rj tov o^vTepov npos to ^apv to avTo. 

^ The nature of concordant sounds is that when they are struck 
or blown simultaneously, the melodic relation of the lower note 
to the higher is identity, as likewise the relation of the higher 
to the lower; but when discordant sounds are struck or blown 
together, there seems to be nothing of identity in the relation 
of the lower note to the higher, or of the higher to the lower.’ 
[Practically the same definition is given by Aristides Quintilianus 
(ed. Meibom, p. 12, 1 . 21), and Bacchius (ed. Meibom, p. 2, 1 . 28).] 

Marquard professes himself unable to find any meaning in 
this definition. The language is certainly not happy; but I 
think the sense is clear enough. If two sounds are discordant, 
when they are sounded together, the particular character of 
each will stand out unreconciled against the other; that is, 
the relation of the higher to the lower or of the lower to the 
higher will not be one of identity in which differences are sunk. 
On the other hand, when concordant sounds are heard together, 



the resulting impression is that of the reconciliation of differences, 
the merging of particular natures in an identical whole. This 
is well illustrated by the concord called the Octave, where the 
relation of identity is so predominant that we regard the notes 
of it as the one note repeated at different heights of pitch. 

According to the Jsagoge (ed. Meibom, p. 8, 1 . 24) ean Sc (rvfi- 
(fxopla flip Kpaais Svo (l>06yyG)p o^vrepov koX ^apvripov* Siacfxopia Sc 
TovpaPTLOp Suo (l>06yy(t)p apn^ia &(tt€ pfj Kpa0rjpaij dXXa Tpaxvp0fjpai 
TTjp aKofjp, ‘ Concord is the blending of two notes, a higher and 
a lower ; discord, on the contrary, is the refusal of two notes to 
combine, with the result that they do not blend but grate on 
the ear.^ The same conception is more clearly expressed in the 
definition quoted by Porphyrius: —(rvpLcfxopia S’ cVri 8voip ^5dy- 
yoi>p o^vTrjTi Kal ^apvrrjri 8ia(f>€p6pTCi>v Kara to avro 7 rr«o*iff Kal 
Kpaais* Scl yap tovs (l>06yyovs (rvyKpov(r0€PTas €P ri erepop eiSos 
(l)06yyov dnoTeXelp Trap eKcipovs c^ (l>06yya}P fj (TvpL(l)(opia yeyopep. 
* Concord is the coincidence and blending of two notes of differ¬ 
ent pitch, for the notes when struck together must result in 
a single species of sound distinct from the notes which have 
given birth to the concord.^ 

The following definition of Adrastus is quoted by Theo. 
Smym., p. 80, and Porphyrius, p. 270, avpLcfxopova'i Sc <^5dyyoi 
Trpos dWrjXovs hp 0aT€pov Kpov(r0ipTO£ iiri tipos dpydpov rap ipraroup 
Kal 6 XoiTTos Kara ripa olKeioTrjra Kal avp.7rd0€iap ovprjxfj* Kara to 
avro Sc a/Lta dp,(j>OT€pa)p Kpova‘0€PT(op Xeia Kal Trpoarjprjs ck Tfjs Kpd^ 
o*ca)ff €^aKov€Tai (jxoprj. ^ Notes are in concord with one another 
when upon the one being struck upon a stringed instrument, 
the other sounds along with it by affinity and sympathy; and 
when the two being struck simultaneously one hears, in con¬ 
sequence of the blending, a smooth and sweet sound.’ 

Most philosophic of all is Aristotle’s definition in Probleins 
xix, 38, (TvpLcfxopia Sc x^ipopLep on KpdaU ian Xoyop e^opTcop 
ipapTicop Trpoff aXXrjXa. 6 pep ovp Xoyoff Tariff, o ^p (f)v(r€i rj8v, ^ The 
reason that we take pleasure in concord is that it is a blending 
of opposites that have a relation to one another. Now rela¬ 
tion is order and we saw that order naturally gave pleasure.’ 
Cp. also Aristotle Trcpi ala‘0rj(r€Ci)9 Kal al(T0rjTa>p c. 3, p. 439 
ra pep yap ip dpi 0 poi 9 evXoyiarois p^pcopara, Ka0d7rep eKel ray 


crvfJLcjxopiaSj to, rfSiara tS>p ;^pa)fiara)i' eivai SoKovpra, ‘The most 
agreeable colours, like concords, depend upon the easily calcu¬ 
lable relations of their ingredients.^ 

Later theorists introduced Trapacjxovos as an intermediate term 
between aviiclxovos and Siac^cai/oy. According to Gaudentius 
[ed. Meibom, p. II, 1 . 30], Trapaxfxovoi Sc oi pecroi pjev (rvpcfxiDPOv Kai 
8ia(l>a)POv* ip Se rfj Kpovcrei (f>aip6p€Poi (rvpcfxopoij fioTTcp ini rpi&p 
TOPCDP (^aiVcToi, dnb napvnarqs piatop ini napafiioTjPj Kal ini Suo 
t6p(op^ dnb piaoDP biaropov ini napapiarjp, ‘ Paraphone sounds stand 
midway between concords and discords; when struck ’ [this 
probably means ‘ when not prolonged by voice or wind instru¬ 
ment, but sounded momentarily on strings’] ‘they give the 
impression of concord; such an impression we receive in the 
case of the interval of three tones between the Parhypate Mes6n 
and the Paramese; and in the case of the interval of two tones 
between the Lichanus ’ [the term ‘ Diatonus ’ is sometimes used 
for Lichanus] ‘ Meson and the Paramese.’ 

The term opjocfxapoi is applied to notes which differ in function, 
but coincide in pitch. Thus the Dominant of the key of D and 
the Subdominant of the key of E fall alike on A. See Aristides 
Quintilianus, ed. Meibom, p. 12, 1 . 25. 

1 . 22. ra (Tvpdera tS)p daypOironp. Aristoxenus means by a 
simple interval one that is contained by two notes between which 
none can be inserted in the particular scale to which they belong. 

Thus in the enharmonic scale. 


interval between /‘and a is simple, because in this scale no note can 

occur between them ; but in the diatonic 

scale the interval between f and a is compound, because in this 
scale g occurs between them. Thus the same piyedos or mag- 
nitudef-a^ which as a piyeOos is of course composite [the simple 
magnitude of music being a quarter-tone], may sometimes be 
occupied by a simple, sometimes by a composite interval. 

1 . 23* rjp Siacfiipei ra prjya tS>p dXoy&p. This 8ia(l)opd is not 
without difficulty. The terms prjrd and aXoya naturally apply to 
quanta in relation to one another. 4 is SXoyop in relation to 7, 
the area of a square in relation to that of a circle. But where 



in the case of an interval are the two quanta the relation between 
which constitutes it rational or irrational? Not inside the 


interval, for Aristoxenus, as we have already seen, has nothing 
to do with the Pythagorean view of intervals as numerical 
relations. An interval then must be rational or irrational in 

virtue of the relation it bears to some quantum outside itself. 
Marquard supposes this quantum to be the twelfth of a tone 
because that is the smallest measure used by Aristoxenus in 
calculating the comparative sizes of intervals. (See p. 117, 
11 . 1-19.) But this supposition, as we shall presently see, is 
directly forbidden by Aristoxenus himself. The true explanation 
is supplied by the following interesting passage from the 
Elements of Rhythm (Aristoxenus, ed. Marquard, p. 413, 29):— 

"'QpiOTaL Se Ta>p 7ro8a>p cKacrTOS r]TOi \6y(o tlv\ rj akoyiq, roLavTTj^ 
ijriff 8vo Koycop yvoapiyuoav alaOrjcrei ava peaop eorai. Tepoiro 
5’ ap TO clprjpipop SSe KaTa(l)aP€S* el Xr^cfydeiTjaap 8vo ttoScj, 6 pLCP ?o*ov 
TO aPd) r<S Kara) €xa}p Ka\ diarjpLOP c/carcpoj/, 6 Se «ro pep Kara} SicrrjpoPy 
TO Se apo} ^piaVj TpiTos Se tls \ri(f>6eLr] ttovs irapa tovtovs^ t^p pep 
Pdcrip tarjp ap tois ap(f)OT€poL9 e^euPy ttjp Se dpaip peaop peyedos 
e^ovaap tc^p apaecop, *0 yap tolovtos ttovs oKoyop pep e^ei to apo) 
Trpos TO Koroy earai S’ fj dXoyia peTa^v 8vo XoyoDP yp(opip(op Trj 
alcrdrjaeij tov re laov Kal tov diTrXaaiov. . . • 

Aei Sc prjS' epTovOa SiapapTeiPj dyporjOepTos tov re prjTOv Kal tov 
aXoyoVy TLpa Tponop eV roiff irepl tovs pvdpovs Xap^dpeTai. ^Qairep 
ovp ip TOis biaaTqpaTLKo'is crToixeioLS to pep koto, peXos prjTop eXri<f>6r)y 
6 irpoiTOp pep eVri peX(o8ovpepoPy enevra ypdypipop Kara peyeOos^ rjToi 
i>s Td re aiipcfxopa Kal 6 topoSj rj a)ff ra tovtois aippeTpa^ to Se fcara 
rovj Td)P dpiOpcop popop Xoyovs prjTOPj cS (Tvpe^aipep dpeX<o8rjT(o elvaC 
ovTco Kal ep roiy pvBpms vTToXrjTrreop e\eip to re prjTOP koI to aXoyoPm 
To pep yap kotcl ttjp tov pvBpov (l>va‘ip Xap0dpeTai prjTOPj to Se 
KaTci Tovs Tcjp dpidpSiP popop Xoyovs. To pep ovp ip pvdpia Xap^apo^ 
pepop prjTOP ;^poj/ov peyeOos irpoiTOP pep Sel tc^p wnTTOPTCUP els ttjp 
pvdpoTTOuap eJpaiy eireiTa tov 7ro86s ip & rera/crai pepos eipai priTOP* 
TO Se KOTci Tovs Tci)p dpidpcop Xoyovs Xap^apopepop prjTop tolovtop ri 
Set poeip olop ip TOLs SiaoTrjpaTLKo'is to 8oi)8eKaTi]p6piop tov topov Kal 
ei rt TOLOVTOP aXXo ip Tais Tmf 8LaaTrjpdT(op irapaXXayaLS Xap^dpeTai. 
^apepop Se Sia Tci)P elprjpepoDPy on fj pecrr] Xri(l>6ela‘a tcop apcreoDP ovk 
eo*rai (svppeTpos Trj j3ao*ef ov8ep yap avTdiP peTpov eVri kolpop 


eppvO^ov. ‘ Every foot is determined either by a ratio (between 
its accented and unaccented parts) or by an irrational relation 
such as lies midway between two ratios familiar to sense. 
This statement may be illustrated as follows: take two 
feet, one of which has the accented and unaccented parts 
equal, each of them consisting of two minims of time, while 
the other has its accented part equal to two minims, but its 
unaccented only half that length.’ [Assuming the minim 
to be, what it once was, the sign of the shortest possible 
musical time, the first of these feet would be of the form 

Q Q , the second of the form | q ^ j*] ‘Now take 

a third foot besides, having its accented part equal to the ac¬ 
cented part of either of the first two, but its unaccented, a mean 
in size between their unaccented parts.’ [Its form will be 

Q ^ . |.] ‘In such a foot the relation between the ac¬ 
cented and unaccented parts will be irrational, and will lie 
between two ratios familiar to sense, the equal,’ [ q : q ] ‘ and 
the double’ [ q ] . . . ‘ Nor must we be led astray here by 

ignorance of the principle on which the conceptions “ rational ” 
and “irrational” are determined in matters of rhythm. In the 
Elements of Intervals we assumed on the one hand a “ rational 
in respect of melody” which is firstly something that can be 
sung, and secondly, something whose size is well known, either 
[directly] as* the concords and the tone, or else [indirectly] as 
the intervals commensurate with these; and on the other hand, 
a “rational in respect of numerical ratios,” which, as a fact, 
was something that could not be sung. A similar view must 
be taken in the case of rhythm, and we must distinguish the 
rational in respect of the natural laws of rhythm from the 
rational in respect of numerical ratios only. According to 
the first reference, a rational time-length is one which, firstly, 
can be introduced into rhythmical composition, and secondly, 
is a rational fraction of the foot in which it is placed. Accord¬ 
ing to the second reference, it must be conceived as something 
in the sphere of rhythm corresponding to the twelfth of a tone 
in the sphere of melody, or to any other similar quantum 
assumed in the comparative measurement of intervals. It is 



clear from these remarks that the mean between the two un¬ 
accented parts will not be commensurate with the accented 
part; for they have no common measure with a rhythmical 

We see here that the reason why the foot I o cj • I is 
irrational is, that though , is a possible rhythmical element, 
and though the relation of ^ , to Q is known as that of 3 to 4, 
yet the length , while mathematically commensurate with 

Q, is rhythmically incommensurate. For their common medstire^ 
being half the minimum time lengthy has no existence in the 
practice of rhythm. 

The case is similar with regard to Melody. If any interval 
can be sung; if its length be readily cognisable, either imme¬ 
diately as a concord or tone, or because it is commensurate 
with one of these, the common ineasure being an actual melodic 
interval^ then it is pr\T6v. If these conditions be not fulfilled, it 
is oKoyov. Thus a twelfth of a tone is not a rational interval 
in respect of melody, because it cannot be sung ; neither is the 
interval of three sevenths of a tone rational; because though it 
can be sung, and though its length can be mathematically 
expressed in relation to a tone, yet the common measure of 
it and of a tone is one seventh of the latter; which is not an 
actual melodic interval. 

1 . 24. ras de Xoinas Cp. Aristides Quintilianus [Mei¬ 

bom, p. 14? 1 * 10], €Ti S’ avTCi>p a fiiv iariv apria, a Sc TTcpirra. 
apria piv ra els i(ra biaipovp^va^ fjpiToviov Ka\ tovos* nepiTTa 
Sc ra els aviaa* Ids at y SicVcij? /cal ttcWc /cal f, and [Meibom, p. 14, 
1 . 20], cri TCdv bia(rTr]paT(ov a pev eariv apaia a Sc nvKvd* ttvkpo, pev 
TCL ekaxiara ods al Sico’ci?, dpaia Sc ra peyiara &S to Sia Tecradpcop. 

P. 109 , 1 . 7. TovTov ye tov rponov /c.r.X. Aristoxenus implies 
by this reservation the possibility of dividing scales into those 
which are composed of other scales (as for instance an octave, 
which is a compound of a Fourth and a Fjfth), and those which 

are not so composed, as for instance -J-J J- - But 

even this last scale, though it cannot be analysed inio other 
scales, is composed of certain parts, namely intervals, and so can 
hardly be called simple. 



1 . 16. dno Tivos fjLcyidovs. The meaning is, ‘ Every scale from 
a certain magnitude upward/ Evidently a scale of a Fourth 
or any smaller scale need not exhibit either conjunction or 

1 . 18. TovTo. ‘This phenomenon of the blending of conjunc¬ 
tion and disjunction.’ 

. €v ivLOLSy i. e. (Tvo'Tjy/Ltao'ii'. Scc lutroductiou A, § 20. 

1 . 19. The term vnep^aTOP signifies that the scale skips certain 
notes which would naturally belong to it by the laws of continuity 
or sequence. See Introduction A, § 26. 

1 . 20. dnXovp Ka\ SlttXovp /c.r.X. Cp. Aristides Quintilianus 
[ed. Meibom, p. 16, 1 . 2], koX rd ph dTrXd d KaS* epa rpoirop e/cKctrai, 
ra Sc ovx dTrXd d Kara 7rX€i6pa}p Tponayp TrXoKfjp yiVcrai. ‘ Single 
scales are those that are composed in one mode; manifold 
scales those that are based on a complex of several modes.’ 

Cp. also Isagoge [ed. Meibom, p. 18, 1 . 20], Sc roO dpera^oXov 
Koi ippera^oXov SioiVci Ka0* tfp Stac^cpct ra OTrXa (rvarrjpaTa tS)p 
anX^iP' dirXd pep ovp carl ra irpos piap picrrjp Tjppocrpepaj SiTrXa Sc ra 
Trpos 8vo, rpiTrXa Sc ra rrpos rpcif, TroXXoTrXdaia Sc ra Trpoff nXeiopas, 
^The difference between the modulating and non-modulating 
scale will be the difference between single scales and those that 
are not single. Single scales are those that are tuned to one 
Mese, double those that are tuned to two, triple those that are 
tuned to three, multiple those that are tuned to several.’ 

The distinctions here referred to we have already considered 
in our comparison of the three ancient Harmonies [Introduction 
A, § 14]. The Mixolydian scale on the old reading of it [Intro¬ 
duction A, § 20] was a (rvarrjpa SlttXovp. 

Cp. p. 131, 11 . 9~io where Aristoxenus contrasts dnXovp and 
pera^oXfiP e^op. 

P. 110 , 1 . 5. XoySScff Ti peXos. For the relation between Greek 
speech and Greek song, see Mr. Monro’s Modes of Ancient 
Greek Music^ § 37. 

1 . 14. I read KaOoXov for Kai nov. Some such word is called 
for by the following iSidriyra. 

1 . 21. on TToXXds ... €p T€ KCLL TavTop K.T.X. Aristoxeuus moans 
that in spite of the great variety of forms that consecution 
adopts, there underlies this variety one immutable law, which 





decides in any case whether any given sounds may or may not 
succeed one another. 

P. Ill, 1 . 7. Tci>p €h TavTo fjpiio(rfjL€P(op is my suggestion for the 
impossible Ta>p els to fjpfioafxipop of the MSS. Aristoxenus is 
obliged to add this qualifying phrase to show that his division 
of the ftcXoff is not inconsistent with mixture of genus. Thus 
the meaning is ‘ every melody that observes one genus through¬ 
out falls into one of the three classes of diatonic, chromatic, and 

1 . 8. ^Toi biaropop ioTLP fj xptapaTiKop /c.r.X. Aristides Quin- 
tilianus (ed. Meibom, p. 18, 1 . 19), gives the following deri¬ 
vations of these names : Enharmonic, otto tov crvvrjppocrdaL^ i. e. 
from the close fitting of intervals exhibited in its Pycnum; Dia¬ 
tonic, € 7 r€iS^ a‘(l>o8pore pop fj (fxopfj Kar avro SiareLPerai (Sidropos is 
to SiareLPO) as (tvptopos to (rvpT€LPG)) ; Chromatic, yap to pera^v 
XevKov Kal peXapos /caXcIrat* ovtco koI to Slcl piatop dp(l)OLP 

6€G)povp€pop XP^P^ 7rpo(r€LprjTaL. 

Cp. Nicomachus (ed. Meibom, p. 25, 1 . 32), /cal €k tovtov ye 
biaTOPLKOP KaXe^Taiy €K tov 7rpox<op€LP 8ia Ta>p t6pg)p avTo popinTOTOP 
Ta)P aXXcop, (p. 26, 1 . 27), &a'T^ dpTiKeiaBai to ipappopiop t© SiaTOPoi* 
pecrop S’ avT<ji)P VTrdpxeip to ;(pa)/xari/cdj/. piKpop yap iraperpe^epy ep 
popop f^piToPiop CLTTO TOV 8iaTOPiKov* cpdep Sc /cal XP^P^ Xeyopep 

Tovs evrpeTTTOvs dpOpiairovs. 

Cp. also the interpolated passage in Aristides Quintilianus 
(Meibom, p. III, 1 . 8), ;(pa)/Ltari/coj/ Sc KoXeiTai rrapd to XP^C^^^ avTo 
TCI XoLTTCL Siao*T^/xara, prj belcrOai Sc tlpos eKeipcop. [According to 
Bellermann (Anony7ni Scriptio^ p. 59) XP^C^^^ Xolttcl biaarripaTa 
= attingere cetera genera ; the pq deladai Sc tlpos eKeipcop is unin¬ 
telligible] . • . rd S’ ipappopiop Std rd ip Tjj tov Siqppoapepov TeXeia 
Siaordcrci Xap^aveaBaC ov yap biTOPov irXioPy oSt€ Sieaecos eXaTTOp 
ipbex^Tai (MSS c’Sc;^cro) /card aiadqaip Xafieip tcl biacTTqpjaTa i. e. 
the Enharmonic genus derives its name from the fact that it 
uses to the full the liberty of variation permitted by the laws of 
Harmony. It uses quarter-tones, than which there is no smaller, 
and ditones, than which there is no greater (simple) interval. 

1 . II. If dpa>TaTop be correct, it means ‘ highest ’ in the process 
of development and so furthest from the state of nature. But 
veoDTOTopy the reading of H, is very tempting; 



1.24. TO fjjev iXdxLCTTop. The Greeks did not recognize the 
Greater or Lesser Thirds as concords. 

P.112,1. II. TO yap Tpls k.tX. Marquard reads p€xpi yap rod. 

1 prefer to read to yap with VbBRS, and am quite willing to con¬ 
strue it either as a direct accusative after Siareivopev (just as we 
can say ‘ to stretch an interval ’ as well as ‘ to stretch the voice 
or as an accusative of length with SiareLPopep used in a neuter 

1. 13. av\a>p. For a full description of the av\6s the reader 
is referred to the exhaustive article of Mr. A. A. Howard, 
in Vol. IV of the Harvard Studies in Classical Philology. 
A few general remarks will suffice here. 

The term avXos commonly denotes a reed instrument of 
cylindrical bore; whether the reed was double-tongued as in 
the oboe, or single as in the clarinet, or whether both these 
forms of mouthpiece were employed, there is no conclusive 
evidence to prove. The musician generally performed on a pair 
of these instruments simultaneously, playing the melody on one, 
and an accompaniment (which in Greek music was higher 
than the melody), on the other. These double pipes were 
divided according to their pitch into five classes, irapBipioi^ 
TraiSiKoLj KiOapKrrrjpLOLj TA.€tot, and wcprAcioi, corresponding 
closely to the soprano, alto, tenor, baritone, and bass ranges 
of the voice. 

1. 15. KaTa(r7raa-6€L(rrj9 ye rrjs avpiyyos. According to the in¬ 
genious theory of Mr. Howard (see last note), the term avpiy^j 
which commonly signifies a pan’s-pipe, was used to denote 
a hole near the mouthpiece of the aiXoy, like the ^ speaker ’ of 
the clarinet, the opening of which facilitated the production of 
the harmonies by the performer. The passages which he quotes 
on the matter are the following :— 

(l) Aristotle (de audib. p. 804 ^), Sio koX t&p dp8pS)p elal Tra^v- 
repai Kal tS)p rekeieup av\S>Pj Kal pdWop oral/ TrXrjp&a'j] tls avrovs tov 
TTP evpaTOs* (fiapepop 8* earip* kol yap &p ttico'i; tis ra (i. e. * if 

one squeezes the reed between the lips or teeth ’) pdXXov o^vrepa 
fl (fxopri yiyperai Kal Xeirrorepay kclp KaTaa 7 rd(rrj ns rds (TvpiyyaSj kov 
8e CTTiXajSiy, TrapTrXeicDP 6 oyKos yiyperai rfjs (fxcprjs 8ia to TrXrjdos tov 
TT pevp^aros Kaddnep Kal dno rSiv naxyrepayp 

R 2 



From this passage, as from the passage of Aristoxenus before 
us, it is evident that the effect of the operation Karaairap rfjp 
(Tvptyya was to raise the pitch of the instrument. 

(2) Plutarch {non posse suaviter, p. 1096 <2), bia tI r&v ’Idoiv av\S)v 
6 (rT€va}T€pos (^6^vT€poVy6 S’ €vpvT€posy ^apvT€pop (l>0€yy€Tai* Ka\ Sia 
tI Trjs avpiyyos dvaaTroapevrjs ndaiv o^vverm Tols (t)B6yyoiSj K\ivop4vrjs 
Sc noKiv ^apvv€i (read ^apvverai) Ka\ a’vvax6€\s irpos top €T€pop 
(^ 0 apvT€popyy SiaxB^is Sc 6 ^vT€pop > From this passage we 
learn that the effect of the operation dpaa-Trdp rfjp aipiyya was 
to raise all the tones of the instrument. 

(3) Anecdota Graeca Oxoniensia^ Vol. II, p. 409, {avpiy^) 

(rrjpiaivfi rfjp onfip tS)P povaiKcdP av\S)P. 

(4) Plutarch (de Musica, p. 1138 a), AvrUa Tr]\€(l>dprjs 6 
M€yapiK 6 s ovTODS cttoXc/xt/o-c rats avpiy^ip, &aT€ tovs avXoTroiovs oiS* 
enideipaL Trinore eiaaep cVl tovs aiXouy, dXXa koI tov IIvBikov dya>pos 
paXiara 8 id ravr dnccTTrj, 

[Mr. Howard gathers from this passage that Telephanes as 
a virtuoso objected to mechanical shifts such as the <Tvpiy^ 
which brought elaborate execution within the reach of poor 
performers. I am rather disposed to think from the context 
that this musician was a lover of the simplicity and reserve of 
ancient art, and resisted innovations in the direction of com¬ 

The only difficulty offered by these passages is in the appar¬ 
ently indifferent use of dpaandv and Karacrirdp to signify the same 
operation (or operations with the same effect). Mr. Howard 
thinks that the avpiy^ might have been covered when not in use 
by a sliding band, which in some instruments was pushed up to 
open the hole, and in other cases pulled down for the same 
purpose. I might suggest that possibly dvaandp and Karaandp 
in these passages are not direct opposites; that Karaandp may 
be used in its primary sense of‘to draw down,' and dpaandp in 
its secondary sense of ‘to open' (being answered in (2) by 
k\lv€lp, ‘ to shut ’). 

Von Jan supposes {Ph7. XXXVIII, p. 382), that the avpiy^ 
was a joint at the lower end of the av\6s which could be 
detached from it. But this view, as Mr. Howard points out, 
does violence to the passage of Aristoxenus before us, as may 


be seen from his own explanation of it. ‘ Der Theil also, auf 
welchem man nach Abnahme der Syrinx weiter blasen kann, 
heisst selbst Syrinx, und das Blasen darauf avplTTCipJ 

P. 113 , 1 . 5. OKTO) is the excellent emendation of Westphal 
for €K tS)v of the MSS. The eight concordant intervals are, The 
Fourth : The Fifth: The Octave: The Fourth and an Octave : 
The Fifth and an Octave : The interval of Two Octaves : The 
Fourth and Two Octaves : The Fifth and Two Octaves. 

11 . 7-12. For Aristoxenus the Concords are the elements of 
intervals, and from them are derived directly or indirectly, 
by processes of addition and subtraction, all the discordant 
intervals. Even the quarter-tone must be thus ascertained: 
From a Fifth subtract a Fourth, and divide the result into 
four equal parts. The latter part of this construction is un¬ 
satisfactory, for how is the ear to assure itself of the equality 
of those parts? It could apparently do so only by such an 
immediate recognition of the interval in question as would 
render any method of ascertaining it nugatory. 

1 . 8. The contrast between the Pythagorean and Aristo- 
xenian views of musical science comes out strongly in the 
definitions of a tone. For the Pythagoreans a tone is the 
difference between two sounds whose rates of vibration stand in 
the relation 8:9; for the school of Aristoxenus, the difference 
between a Fourth and a Fifth. The latter explain the pheno¬ 
mena of music by reducing these to more immediately known 
musical phenomena, the former by reducing them to their 
mathematical antecedents. 

T^v TrpoDTODv avp,(l)oi)vci)v» That is, the Fourth and Fifth. 

1 . 18. For KoKovpj^vov TO, T€ nXeiara of the MSS I read kot^xo^ 
pL€vov ra y€ nXeiara. If KoKovpL^vov be retained it necessitates the 
insertion of the phrase Sia rea-aapoDv, to give it a meaning; 
similarly, vno TeaaapoDv <^ 5 dyyQ)i/, being left without any con¬ 
struction, calls for some such word as Karexopevov. 

ra ye nXelara. Usually, not always; see note on p. 115, 1 . l. 

1 . 20. TLva dri rd^Lv . . . Kipovvrai, This is undoubtedly, as 
Westphal has pointed out, a marginal scholium that has crept 
into the text and displaced the conclusion of the preceding 
sentence. Observe the use of elai instead of eori. 



1 . 21. For the meaning of the terms ^variable’ and ^fixed’ 
notes, see Introduction A, § 8. 

P. 114 , 1 . 14. TovToav §€ TO fi€v tkaTTov K.T.X. Accordittg to 
Marquard’s explanation (accepted by Westphal) of this difficult 
sentence, to tXarrov and to fiel^ov are used by brachylogy for to 
‘ ovK ekaTTov a(f)i(TTaTaLf* and to ‘ ov a(l)i(TTaTaLy and thus 

repeat the cXottoi^ and fxelCov of the preceding sentence. Against 
this it may be urged that the brachylogy is a very violent one; 
and also that on this interpretation the latter clause of the sen¬ 
tence implies that the existence of a Lichanus further than two 
tones from the Mese was a matter of dispute. But of such a 
Lichanus we have no evidence. Mr. Monro would avoid the 
latter difficulty by supposing to to be used illogically in 

the sense of ^ the question of the greater limit.’ 

I consider that the misinterpretation of this passage is due to 
the natural but false assumption that to ekarrov refers to the cXot- 
Tov of the preceding sentence. On my view tovtcdv = tovt<ov tg^v 
diacrrrjfjidTCOv = toO Toviaiov diaaTrjfjLaTOS Ka\ tov dirovov : the geni¬ 
tive is a partitive one ; to ekarrov tovt(i)v {tS>v SLaaTrjfmTayv) and 
TO fi€l^ov rovTGiv mean respectively the tone interval and the 
ditone interval. The general object of the sentence beginning 
at TovTGiv is to justify not the smallness but the largeness of the 
localization of the Lichanus. In fact Aristoxenus would say, 
‘The interval between the Lichanus and Mese cannot be less 
than one tone or greater than two tones. The lesser of these 
distances (which I have assigned as the minimum limit of the 
space between the Lichanus and Mese), is found in the Diatonic 
genus, and is consequently of unquestionable legitimacy; the 
greater of these distances (which I have assigned as the maxi¬ 
mum limit of the space between the Lichanus and Mese) is 
admissible, though often disputed in the present day, and was 
the distinguishing feature of the Ancient Enharmonic music.’ 

1. 15. ovx is plainly wrong, as is seen from the following 
avyx<^poir av. 

1. 16. iiraxOevTGiv. €7rdy€ip means to lead one on to the 
recognition of a general principle through the consideration of 
particular cases. Hence inayony^ = induction. 

P. 115 , 1 . 1 . TOiv dpx^ouKGiv TponcDV Tois T€ TTpinToii Kal TOis ScvTepois. 



Besides the enharmonic scale of the form 


there was another enharmonic scale (commonly called after its 

inventor Olympus), of the form 

which in¬ 

troduced but one note of division into the tetrachord. It is 
possible, as Marquard thinks, that these two scales are here 
referred to as the earlier and later of the ancient modes; but 
the phrase is a strange one. 

1 . 3. ol fjLEv yap fc.T.X. Aristoxenus here records the fact, 
familiar to us from other sources, of the gradual extinction of 
the old enharmonic music. The intervals it employed were so 
fine and required such delicacy of ear and voice, that it can 
never have been popular. But, as we saw in the Introduction A, 
§ 6, the cause which not only accounts for but justifies its 
abandonment is the necessarily imperfect determination of its 
intervals. Aristoxenus himself was quite aware of this deficiency, 
though not alive to the seriousness of it. In a passage quoted 
by Plutarch (de Muszca, cap. 38, 1145 B), after assigning as one 
cause of the disuse of the enharmonic music the difficulty of 
hearing such a small interval as a quarter-tone, he proceeds to 
suggest another explanation, etra koX to pfj Sivaadai XrjcpOrjvai dia 
(Tvpxfxovias TO piyedos Ka6dn€p to t€ fjpLTOVLov Kill tov tovov koI tcl 
XotTra §€ T^v ToiovTiav 8iaaTrjpdT0i)v. * Besides, there is the fact that 
the magnitude of this interval (i. e. the quarter-tone) cannot be 
determined by concord, as can the semitone, the tone, and the 
like.’ For this important principle of the determination of 
discordant intervals by concord, see pp. 145, 146. 

1. 6. yXvKaiueiv. Anonymus (§ 26) contrasts the Diatonic 
genus as ‘ dv8pLKdiT€pov . . . #cat avarrjpoTepov ’ with the Chromatic 
as ^ ^diCTTOV T€ Kai yoepayTOTOpJ 

1 . 20. The subdivisions of the genus are called or 

^ shades.’ See note on p. 116, 1 . 4. 

P. 116 , 1 . I. For convenience, the word Pycnum will be 
retained in the translation to denote the sum of the two small 
intervals of the tetrachord, when that sum is less than the 
remainder of the Fourth. For the meaning of the term see 
p. 139,11. 29-30. 



P ycnum 

In the Enharmonic tetrachord J '■ ■ the 

sum of the intervals between e and x^, and between e and 

/ is a Pycnum, because it is less than the interval between f 
and a. 

^ P vcnum 

For the same reasons in the Chromatic 


tetrachord the sum of the intervals between e and /j and f 
and is a Pycnum. 

But in the Diatonic tetrachord 


is no Pycnum, for the sum of the intervals between e and and 
f and g is greater than that between g and a. 

1 . 4. TovTcov S’ ovT(os K.T.X. We have already seen that the 
Greeks recognize three genera, differentiated by the magnitudes 
of the intervals into which they divide the tetrachord; and we 
have given as the plan of the Enharmonic, quarter-tone, quarter- 
tone, ditone ; of the Chromatic, semitone, semitone, tone and 
a-half; of the Diatonic, semitone, tone, tone. But it will 
immediately be asked, ^Are not other divisions intermediate 
between these equally permissible? Why not for instance 
divide your tetrachord into third of a tone, third of a tone, 
eleven-sixths of a tone ? Or into five-twelfths of a tone, semitone, 
nineteen-twelfths of a tone?’ Certainly, Aristoxenus replies, 
the possible divisions of the tetrachord, the possible locations 
of the Parhypate and Lichanus, are as infinite as the points of 
space. But the ear ignoring the mathematical differences 
attends to the common features in the impressions which these 
divisions make upon it, and constitutes accordingly three genera, 
the Enharmonic, Chromatic, and Diatonic, subdividing the 
latter two again into that is colours or shades of distinc¬ 
tion ; the Chromatic into the Soft, the Hemiolic and the Tonic ; 
the Diatonic into the lower or Flat, and the Sharp or higher. 
It is evident then that each of these subclasses covers many 
differences of numerical division; but one division is taken by 
Aristoxenus as typical of each. 

The exact proportions of these typical divisions are exhibited 


in the following table in which the tetrachord is in each case 
represented by a line divided into thirty equal parts, each part 
consequently being the twelfth of a tone. The places of the 
Parhypate are definitely marked as they are given in pp. 141,142; 
in thSs present passage their positions are less accurately stated. 

Tabl? of the Genera and Shades. 

f ^ , = one-twelfth of a tone. 

j ^ ^ ^ ^ = a quarter-tone, or the least Enharmonic diesis. 
r ^ ^ ^ ^ ■ = a third of a tone, or the least Chromatic diesis. 

^ semitone. 

1 2 3 4 5 6 T 8 9 10 11 12 = 2) ' 

f— T ' I I I ■!-1—1- 1 ' I r I I “ lunc. 


Parhypate Lichanus 

1 2 3 I 4 5 sir 8 9 10 11 12 13 14 15 16 IT 18 19 20 21 22 23 24 25 26 27 28 29 30 

r" n I " ■■ T T ' 1 f nr !'■ ' 1 r i r ■ i i t i I i i i t ■ m ^ i ■ ! r ^ 


Chromatic (soft) 

Parhypate Lichanus 

2 3 415 6 7 8 I 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 

V *1' 1 ' I ' " I r - r ' T ■' ^ I I I n " T i - i i i - i * i i n* T i T t ■ i 

Chromatic (Hemiolic) 

Parhypate Lichanus 

1 2 3 4 Is 6 7 8 9 110 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 

t ■ < ' * 1 ' » I 1 r I ^ ■' ! r ' I ■ 1' 1 r I r t i i i i i t t t i i i' i 

Chromatic (Tonic) 

Parhypate Lichanus 

1 2 3 4 5 6 I 7 8 9 10 11 12 1 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 

t-i"!*'! 1 I M r~ t I 'r-' T ' 1 I r t-'t i r r i i i 'T r r i' i f- T— 

Diatonic (flat) 

Parhypate Lichanus 

1 2 3 4 5 6 I 7 8 9 10 11 12 13 14 15 1 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 
I !■ ' I r 1 I 1 ‘t *1 I T* ■' T T r ^ M T* ' ! ■ r ■ ! i r i r r i i r » 

Diatonic (sharp) 

1 2 
T ' 

Parhypate Lichanus 

3 4 5 6 I 7 8 9 10 11 12 13 14 15 16 17 18 1 19 20 21 22 23 24 25 26 27 28 29 30 

I ' f » " 1 I I I T" r r r ■ I i r r ' 8 t r t t -r r ■ r t- t i i ■ 

1. 19. TO ^the particular species of chromatic.’ fjfjii- 

6 \lovj ^ in the ratio of three to two ^; because this was the 



relation between the Pycnum of the Hemiolic Chromatic and 
the Pycnum of the Enharmonic scale (9 and 6 respectively in 
the above table). 

P. 117 , 1 . 4. Set yap k.tX These words are followed in some 
of the MSS by a detailed proof of the fact that the thifd of 
any quantity exceeds the fourth of the same quantity by a 
twelfth. It runs as follows: ineidfinep 6 touos €v piv 
Tpia SiaipciTaiy to Si TpiTrjpopiov KoXeirai ;(pQ)/iaTtKJ7 SUais* iv dp-- 
povia Si els S {riaaapa M) Siaipeiraiy to Si rerapTrjpopiop (S popiov M) 
KakeiTai dppopiKrj SleaiSy to ovv Tpirrjpopiov (y popiov M) tov avrov 
KOI ivos TOV T€TapTrjpopiov (S popiov? M) tov avrov SioSeKarip vnep- 
o\ov 0)9 €7rl TOV 1)3. av SiiXca top ijS els y. S. koI ttoKiv 
TOP avTov 1)3 els S.S (S. y. restituit Marquard), iv piv Tfj els y. 8. 
Siaipeaei yivovrai re(r(rapes TpidSes, ev Si rfj els S, S, (S. y. restituit 
Marquard) rpels rerpdSes. vnepex^t’ ovv rj S rrjs y. S. (y restituit 
Marquard) to Tpirqpopiov tov rerapTripopiov povdSi, onep eari tov 
oXov SaySiKaTov. Marquard very properly relegated this gloss 
to the Critical Commentary. 

P. 118 , 1 . 3. dneipovs top dpidpov. Aristoxenus means of 
course not that there can be more than one Lichanus in any 
one scale, but that, given any note and its Fourth above as 
boundaries, one can constitute an infinite number of scales 
differentiated by the positions of their variable notes, that is 
of their Lichani and Parhypatae. 

1 . 15. Marquard, followed by Westphal, changes the order 
of the sentences here and reads Koivayvei yap ra Svo yeprj tS)v 
napimarOiv —6 8’ erepos 18109 tyjs dppovias, on the ground that the 
former sentence gives the explanation of 6 piv koivos tov re Siarovov 
Kai TOV xp^p^Tos and so must immediately follow it. But the MSS. 
order is correct. Koiviovel yap k.tX. explains not the phrase 6 piv 
Koivds K,T.\.f but the principal sentence TrapvnaTrjs Si Svo el(ri rowoiy 
and 6 piv koivos . . . tyjs dppovias is a parenthesis. The sense 
is, ‘The loci of the Parhypate are not three, like those of the 
Lichanus, but two (one common to two genera, and one par¬ 
ticular) ; for the Chromatic and Diatonic have their Parhypatae 
in common.’ 

For ra Svo yevrj compare p. 126, 1 . 8, ov yap enpayparevovTO nepi 
TOiv Svo yeva>Vy dWd irepi avTrjs tyjs dppovias. 



I . 17. There are two loci of the Parhy- 

pate; the line 4 in the above table, which is peculiar to the 
Enharmonic genus, and the line consisting of 5 and 6 which 
is common to the Chromatic and Diatonic. The meaning of 
this last assertion is that the Diatonic and Chromatic genera 
borrow one another’s Parhypatae, so that you may melodiously 
combine in a tetrachord any Parhypate in 5 and 6 with any 
Lichanus in the lines from 8 to 18 inclusive with this important 
exception however that the lowest interval of the tetrachord must 
never be greater than the one above it. See Introduction A, § 7. 

II . 18-21. Of this most important law Aristoxenus offers no 
proof beyond an appeal to the ear— yiyuerai yap IppiKes Terpa’- 
XOpSoV K.T.X. 

I. 21. avKTov ap(f)OTlp(os^ ‘ unequal in both ways ’ that is ‘ greater 
and less.’ 

II . 23, 24* The substitution of napvnaTrjs re xP^P^tikyjs ^apv^ 
tAtyjs for the napvTraTrjs re ;(pQ)/iaTtK^9 TrapVTraTrjs of the MSS 
completely restores the sense. Aristoxenus proves his state¬ 
ments that the Chromatic and Diatonic genera borrow each 
other’s Parhypatae by appealing to the extreme case. A melo¬ 
dious tetrachord is obtained from the combination of the lowest 
Chromatic Parhypate, and the highest Diatonic Lichanus. 

P. 119 , 1 . 2. I retain the reading of MVBRS. 

Aristoxenus means that he has exhibited the extent of the locus 
of the Parhypate, both as divided into the loci peculiar to 
certain genera and colours, and as a whole embracing all those 
divisions. In p. 115,1.19, he says that having determined the loci 
as wholes {touv oXodv tottcoi') he must proceed to determine their 
divisions according to genus and colour. Here he sums up his 
account of the locus of the Parhypate by stating that he has 
dealt with it from both these points of view. 

Marquard, followed by Westphal, reads ivredeU, and trans¬ 
lates, ‘The locus of the Parhypate is clear (from the above 
remarks) as to its division and its place of insertion.’ But this 
translation conveniently ignores the words 00-09 cWiV, which 
show that the size of the locus is what is here considered ; and 
the space of a locus is not affected by its place. 

1 . 15. Aristoxenus here returns to his criticism of the method 



of KaTaTTVKvaxTis (cp. note on p. loi, 1. i), and shows that it 
supplies a false conception of musical continuity or sequence; 
in other words, that it gives a false answer to the question, 
‘ Starting from a given note, how are we to determine what 
is the next note to it above or below?’ For it ignores the 
dvvafiis of the given note, that is, its function in the system 
of which it is a member; and regarding it merely as a point 
of pitch, it declares that the next note to it is that point of 
pitch which is separated from it by the smallest possible interval. 
But Aristoxenus sees that though there may be a certain truth 
in this answer from the point of view of Physics, it is musically 
absurd. Let us take the note^ and ask what is the next note 
above it. But for the purposes of music f is nothing except 
as a member of a system or scale, and the question of the next 
note to it is meaningless until its function in a scale is deter¬ 
mined. Let us then restate our question thus: ‘ what is the next 
note above an f which is the second passing note in an enhar¬ 
monic scale ascending from ^ ’ Now the answer to this cannot 
be yfy as the theory of KaTaTrvKvodais would lead us to believe; 
for that would imply the possibility of singing three quarter- 
tones one after the other; whereas it is a law of the voice, and 
consequently a law of music, that only two dieses can occur in 
succession. In fact, the theory of KaTa7rvKvoi)(ris in its complete 
application would imply the possibility of singing in succession 
as many quarter-tones as are contained in the whole compass 
of the scale. 

1. 19. ovx oTi like ovx oTTcos is an elliptical phrase signifying 
‘not to speak of,’ and is used for ov fiovov ov. Cp. p. 130, 1 . 7, 
ov yap oTi iripas Ttjs dppx)viKrjs. The corruption of the MSS 
reading here might be traced through the following stages; the 
insertion of ov after on by a scribe who, ignorant of the ellipse, 
felt the want of a negative ; the misreading of on ov as tov ; 
the consequent change of Svparop to Svpaadai to supply an 
infinitive for the article, the addition of pr) to supply the place 
of the lost ov ; the change of /ieXwS^crai to to explain 

Tfj (fxaprjy the true construction of which had been hidden by 
the corruption of dvparop. 

Sieaeis okto) koI eiKoaip, Why twenty-eight quarter-tones 


and not rather twenty-four, seeing that there are six tones 
in an octave ? Because some scales, such as the Dorian, con¬ 
sisted of seven tones. See Introduction A, § 20. 

1 .24. rj fiiKp^ K.T.'X. This seems to be a somewhat contemptuous 
reference of Aristoxenus to the fact that in strict mathematical 
accuracy a Fourth is not quite two tones and a half. As we 
have often seen already, Aristoxenus is concerned with musical 
phenomena with a view to their artistic use, not their physical 

P. 120 , 1 . 2. ov 7rpo(r€KT€ov 61. Marquard retains the reading 
of the MSS and translates ‘Nicht also ist fiir die Aufeinanderfolge 
darauf zu sehen, wann sie aus gleichen, wann aber aus unglei- 
chen entsteht.’ But ore is relative usually, demonstrative some¬ 
times ; but never interrogative. 

The general meaning of the passage is clear. The nature 
of melodic consecution, Aristoxenus would say, cannot be ex¬ 
pressed by any law enjoining a succession of so many equal 
or so many unequal intervals. Thus, we cannot say, ‘Two 
equal intervals must be followed by two unequal,’ for while this 
rule is fulfilled by the Enharmonic scale, it is violated by the 
Diatonic, which has three tones in succession. Nor can we 
say ‘ three equal intervals may follow one another ’; for while 
this is possible in the Diatonic genus, it is impossible in the 
Enharmonic. [Cp. p. 143,11. 21-23.] Translate, ‘ We must not 
fix our attention on the fact that in certain cases,’ &c. 

1 . 13. I read yuerd for fih of the MSS. p,€p is out of place, 
as there is no antithesis between this assumption and the 
following; and some preposition is required to give a con¬ 
struction to TO TTVKPOV . . . (TVtTTrilXa. 

1 . 16. vTroK€L(T 6 (o §6 KOI Ta)p i^rjs K.T.X. Here Aristoxenus states 
for the first time his fundamental law of continuity; that if a 
series of notes be continuous, any note in that series will form 
either a Fourth with the fourth note in order from it above or 
below, or a Fifth with the fifth note in order from it above 
or below, or will fulfil both these conditions. 




is a legitimately continuous scale. A, though it does not form 
a Fourth with c, forms a Fifth with e; By though it does not 
form a Fifth with xe, forms a Fourth with e ; xB does not form 
a Fifth with but forms a Fourth with xe\ c does not form a 
Fifth with <2, but forms a Fourth with f\ e forms a Fourth with 
a and a Fifth with b ; and so on. 

On the other hand, 

is not a legitimate scale; for b forms neither a Fourth with 
nor a Fifth with f. 

1 . 22. 0)9 €771 TO TToXu i. 0. in the Enharmonic and Chromatic 
scales, but not in the Diatonic. 

1 . 25. ivavTi(ds TiOeadai #c.t.X., to. dvo laa are the two equal 
intervals of the Pycnum: ra dvo aviaa are (i) the complement 
of the Fourth and (2) the disjunctive tone. Now in the scale 
descending from the Pycnum 

the disjunctive tone lies next the Pycnum, and the complement 
of the Fourth second from it; while in the scale ascending from 
the Pycnum 

we find the complement of the Fourth next the Pycnum, and 
the disjunctive tone second from it. 

P. 121, 1 . 5. Every compound interval can be analysed into 
simple intervals but not into simple magnitudes. Thus, a Fourth 


in the Enharmonic scale is analysed into quarter-tone, quarter- 
tone, ditone. Now quarter-tones are simple intervals and simple 
magnitudes at the same time; for quite apart from any con¬ 
sideration of systems or scales, no smaller musical magnitude 
than a quarter-tone exists for ear or voice. But the ditone 
though a simple interval in this scale, since the voice in this 
scale cannot, is not by any means a simple magnitude. 
For if we abstract rom consideration of systems and scales, a 
ditone as a space is obviously reducible to two tones, and 
even farther. 

1 . 7. This passage is quite corrupt in the MSS. I read 
aKpcav for €v for eV, and e<T<d6ev for e^(o6€p ; insert hv after 

(f)d6yyoi)Vy and omit it after a/cpcoj/, and insert eKacrrov before 

It must be remembered that of i^rjs (fjdoyyoi are not neces¬ 
sarily consecutive or immediately successive notes; the phrase 
applies equally to notes that are in the same line of succession 
even if at a distance from one another. Thus, in our major 
scale of C, the notes are because members of 

the same legitimate scale. Now an is a sequence of 

consecutive or immediately successive notes, and this could 
not be expressed by saying merely that it proceeds Sid tS)v 
( f)duyyoi)y. The further necessary qualification is given by 
the following words: the successive notes must be separated 
from one another by simple intervals; must, in other words, 
be the nearest possible notes to one another in their scale. 

Direct sequence is a species of sequence in general. Thus 

is a sequence, but not direct; 

is a direct sequence. 

€(roi)d€v tS)v aKpodv means ‘within the extremes,’ that is ‘between 
the first and last notes.’ The first note of a sequence is not 
preceded, the last note not succeeded, by a simple interval. 
[Mr. Monro would retain e^oidep in the sense of ‘except.’] 



P. 122 , 1 . 10. TovTiiiv. For ovTos in the sense of istcj cp. 
p. 132,1. 24. 

1 . 13. There may be an allusion here to such a doctrine 
as we find in the Philebusy or possibly to iripas may be an ac¬ 
cusative in apposition to the following sentence, and mean ‘ as 
the sum or final conclusion of the matter.’ In the latter case 
I should prefer to read rayaOov. 

1 . 20. Marquard quite unnecessarily reads €Lkrififi€vrf for 
etprjfiivTjy and gives the following reason for the change ; ^ Kann 
man denn eine prior opinio griechisch einfach eine elprjpevrf 
vnoXrjyl/is nennen, wenn vorher von einem Aussprechen gar 
keine Rede gewesen ist?^ fj etprjpievrj vjroXtjylri^ refers back to 
vnoXap^dvovra of 1 . 9 * 

P. 123 , 1 . I. o)ff 6^);. The MSS read ©9 €(I>tjv which Marquard 
retains, translating ‘ aus den genannten Griinden.’ But €(l)riv 
is not the same as as dnovy and must refer, not to airas ravras 
rds alriaSy but to Si* airas ravras rds alrias TrpoeX€y€ ^ApiaroT^rjSy 
and Aristoxenus has not said that. 

1 .11. Marquard ruins the sense of this passage by his insertion 
of Kai between on and Kad* oaopy and his mistranslation of oiS* 
aKovaairres oXods —‘ das aber, dass die Musik und in wie weit sie 
niitzen kann, verstehn sie gar nicht.’ The sentence to S’ oti ... 
(oc^eXeiF is elliptical. The complete statement which Aristoxenus 
had made was on fj pev roiavrr] pov(riKrj ^Xdnrei fj Se roiavrr) 
(o^cXei, KaS* Strop povtriKrj dvparai d}(f>€X€ip. The careless listeners 
just caught the first part of the statement oti fj pep . . . toi- 
avrri ox^fXei : the concluding qualification on pev . . . roiairrj 
wc^eXei] Kad^ oaop povtriK^ Svparai oixjyeXeip escaped their ears 
altogether. In such a sentence as this on serves the same 
purpose as inverted commas in English. 

Westphal rewrites the whole sentence and destroys its 

1 . 13. I read epneipoi for arreipoi. If dneipoi be retained we 
must suppose a deficiency in the MSS. Marquard supplies it 
by inserting dypoeip npotreitrip after etrrip. As he translates 
‘ kommen aber herzu,’ it would seem that he has confused the 
forms of elpi and eipi. 

1. 15. as vvv exei of the MSS is meaningless. The present 


condition of the science has nothing to do with the argu¬ 

1 . 18. vTrdpx^i KaOdrr^p del Xey^rai. Marquard retaining the 
^of the MSS translates ‘many other things are indispensable 
to the musician than those that are constantly said to be so ’; 
but both the grammar and sense of this sentence are doubtful. 
Is there any evidence or any likelihood that there was 2iperpetual 
misunderstanding of the qualification of a musician? Would 
not TToWa €T€pa rj mean ‘ many things different from ’ rather than 
‘ many things in addition to ’ ? And why not erepa tj a rather 
than €T€pa rj Kaddmp. Kaddrrep del Xeyerai, if we omit the means 
‘as we consistently assert’ [see, for example, p. 95,11. I3-I5]- 
For a similar use of the present passive of Xey©, cp. p. 130, 1 .16, 
oTi S’ dXrjdrj TO, Xeyd/xem, ‘ that our assertion is true ’; also p. 153, 
1 . 6. Westphal secures the right sense by the clumsy insertion 
of TovTo after 

P. 124 , 1 . 2. In this paragraph Aristoxenus defines his 
position in relation to the question What is the foundation of 
musical science ? On the one hand, he rejects the intellectual 
or mathematical theory of the Pythagoreans on the ground that 
the principles, from which they seek to deduce the facts of 
music, lie outside the sphere of music altogether, and fail to 
account for those facts. On the other hand, he rejects equally 
the blind empiricism which takes the single facts and registers 
them without any attempt to ensure completeness, or ascertain 
the general law. See Introduction B, § 2. 

1 . 17. Let us suppose that as we are listening to a passage 
of music in the diatonic scale 

this musical phenomenon, what faculties must we employ? 
In the first place we obviously require our sense of hearing 
to tell us that a semitone has been sung; but that is not 
enough. We require our intellect also to form a conception 
of the system in which the e and /occur, and to identify their 

S 257 



functions in it; so that the phenomenon before us may be for us 

something quite distinct from the passage from 


in the enharmonic scale 

1 . 18. Ta>p (fidoyyoDv, Toirayp t)f the MSS is wrong. The 
diacTT^fxaTa Aristoxenus always regards as mere distances ; 
functions he attributes only to the notes. Cp. p. 127, 1 . 3, ovk 
avrapK-q ra diaarfipLaTa x.t.X. 

Svvdpeis. dvvapis signifies the function which a note dis¬ 
charges in relation to the other notes of a scale. Thus in 
modern music the divapis of 6 is that of a leading note in 
the key of c, that of a dominant in the key of that of a tonic 
in the key of d. 

P. 124 , 1 . 22-P. 125 , 1 . 2. Marquard and Westphal have com¬ 
pletely missed the meaning of this passage. t£ povaiK^ is not 
the musician in the sense of the musical artist; nor is Aristo¬ 
xenus labouring at the obvious fact that keenness of sense 
is a szne qua non of artists in general as distinguished from 
students of science, p,ov(rLK<a is the student of musical 
science; and the point to which Aristoxenus would draw our 
attention is that Music presents us with a science for which 
accuracy of sense is indispensable. In this respect musical and 
geometrical science differ from one another. The propositions 
of Geometry are deduced from principles which, though possibly 
in the last resort principles of sight in the sense that without 
sight we never could have conceived them, are yet so abstract 
and fundamental that their acceptance accompanies the lowest 
use of that faculty. But the principles of musical science rest, 
not on the presuppositions of hearing in general, but on the 
evidence of the developed and cultivated ear. That a straight 
line is the shortest distance between two points may be a prin¬ 
ciple of sight in the sense that ‘ straight,’ ‘ distance,’ ‘ two,’ &c. 
are phenomena of sight; but it does not require sharp eyes to 
apprehend it. On the other hand Aristoxenus* proof of the 
magnitude of the Fourth [pp. 146-147] depends on an appeal 


to the ear, by no means universal, that can distinguish a concord 
from a discord. 

P. 126 , 1 . 6. From consideration of the faculties Aristoxenus 
turns to the object matter which those faculties are to appre¬ 
hend. Of this object matter he finds the all-pervading 
characteristic to be identity under difference, the co-existence 
of a permanent and a changeable element; and cites in support 
of his statement several cases which may be made clearer by 
the following illustrations: 

(l) 1 . 7 - \€\j6i(0£ yap k.t.X.]. 



Here we have as permanent element the relation between the 
fixed notes ; as changeable the position of the intermediate notes. 
(2) 1 . 8. [TraXii; orav pevovros k.t.X.]. 


Compare the interval between E and Ay and the interval 
between 6 and e. Here we have as permanent the magnitude 
of the intervals (a Fourth); as variable the bvvapis of the notes 
containing the interval. 

(3) 1 . II. [#cal ndkiv orav tov airov peyidovs x.T.X.j. 

Here we have the same magnitude, a Fifth, appearing in two 
different figures, that is with its intervals arranged in different 


(4) 1 . 13. [oxravTCDff Se xal orav ic.t.X.]. 

In the two scales 



S 2 



compare the tetrachord between b and e in the former, with 
that between a and d in the latter. Here we have as 
permanent the size and figure of the interval; as variable the 
function of the tetrachord which in one case is modulating, in 
the other, not modulating. 

(5) 1 . 16. [koI yap fxeyovTOs TOu \ 6 yov ic.t.X.]. 

Compare the three following feet or bars : 


ro SaKTvXiKop 
yiyofy TO iv 


^ J J 


€y oKraafjfjLa pcyc^ei 

(taking the crotchet as the unit). 

€V €^a(T^fi(^ fk^ykBn. 

€V T^Tpaarjfita fieykd^i. 

In these three we have as permanent the Dactylic character 
with its ratio of equality between the arsis and thesis; while the 
lengths of the feet differ, their difference being due to the different 
rate of movement. 

(6) 1. 18. [ Kal tZhv fx^yidSiv pfvovTcav k.t.X.]. 

Compare the two following bars or feet: 

TO daKTvXiKov ykvos to iv tw 
X(r(f \6y<p 

TO lap^iKov yivos to iv tS 
Si7rXa(ri© Xoy© 

Here we have the piyedos permanent, six crotchets; but the 
genus varies, the first being ^ dactylic * with the arsis equal 
to the thesis, the second being ‘ iambic ’ with the arsis double 
the thesis. 

(7) 1. 19* avTo fiiy€0os noba ic.r.X.]. 

Compare (a) and (b). 

j- jjj 



iv payidei. 

J J 

Here the same quantity, eight crotchets, appears in (a) as a single 
foot, in {b) as a pair of feet. 

(8) 1. 20. [ai 8ia<^opai . . . 8iaLp€(T€(ov]. 

The same magnitude, say | IWI | may be divided into two 


semibreves, or four minims, or one semibreve and two minims, 
or eight crotchets, or one semibreve, one minim, and two 
crotchets, &c. 

(9) 1- 20. [at bia<l)opai • • • (r;^fidra>i']. 

Let us suppose a certain magnitude, say of three crotchets 
divided into a minim and a crotchet, these parts may be arranged 

in the order J A or in the order ^ ^ . 

(10) 1 . 21. [kQ^oXoU S* €l7r€lV fC.T.X.]. 

In general, rhythmical science reduces the infinite Variety and 
multiplicity of verse to combinations of a few primary elements, 
namely feet. 

1 . 10. The omission of yap, suggested to me by Mr. Buiy, 
restores the construction of this sentence. 

P. 120, 1. 20. I have changed the MSS yivetn to /xeXco-i. 
The corruption might easily be explained both e rei materia 
and also through the proximity of yiyvopivais. For the plufal of 
li(ko9 used of the concrete, cp. p. 130,1. 2. 

yiv^ai is plainly wrong. ‘ That we must distinguish the 
genera if we are to follow the distinctions that occur in the genera ’ 
is an absurd tautology. A comparison with p. 126, 1 . 25, ov 
S ayvo€iv #c.t.X. makes clear the meaning of Aristoxenus’ warn¬ 
ing :—‘ if we neglect the scientific determination of any differ¬ 
ence, we shall fail to detect the concrete cases of that difference 
which meet us in any musical composition.* 

[Since writing this note I have discovered, in collating the 
Selden MS, the letters peX crossed out before yev^ai.] 

P. 127 , 1 . 3. inci S’ ioTiv ovK K.r.X. For example, part of the 
connotation of the terms Mese and Hypate is that they are the 
upper and lower boundaries of a Fourth; but more is required 
to determine the conception of these notes ; for the same might 
be predicated of the Nete and Paramese. 

1 . 8. See Introduction B, § 2. 

1 . 14. ovb€T€pov .. . tS>u TpoTTiov, Onc mcthod is to exhaust the 
acts by a faithful enumeration ; the other is to deduce the facts 
from the principle on which they depend. 

1 . 24. Pythagoras of Zacynthus was the inventor of a stringed 
instrunient called the Tpinovs. See Athenaeus, xiv, 637. 



1 . 25. Agenor of Mitylene is quite unknown. See Porphyry, 
p. 189. 

P. 128 , 1 . 6. TrifinTov 8* carl k.t.X. On the whole paragraph 
cp. Introduction A, §§ 22-26, where I have explained also the 
uncertainty as to the key of the Mixolydian mode. 

1 . 19. rpial di€(T€(Tiv. The separation of keys by intervals of 
three quarter-tones would be an application of the principle 
of KaTa7rvKvoi)(Tis. Cp. note on p. loi, 1. i. 

P. 129 , 1 . 4. fi€Ta^o\rj9. The modulation with which Aristo- 
xenus is here primarily concerned is the fiera^oK^ arvarrjfiaTiKTf 
which is thus defined by Bacchius [ed. Meibom, p. 14, 1 .1], orai^ €k 
rov v 7 roK€ip.€Vov avarrifiaros 619 ?T€pop avarrjpa avax<^p^o‘ri f} peXtoSia 
€T€pap p,e<Tr)p Karao'#c6vafovo'a, *the transition which a melody 
makes from one scale into another by providing for itself a dif¬ 
ferent Mese.’ But a different Mese can mean nothing else than 
a tonic of different pitch, so this transition means simply modu¬ 
lation into a different key. The conditions of its possibility 
are given in the following passage of the Isagoge [ed. Meibom, 
p. 20,1. 33] 

Tipoprai Si ai pLira^oXal otto Trjs fjpuTopLaias ap^dp,€pai piixpf- tov 
Sid natrSyPf &P al p,ip Kara (rvpL<l)ci)pa yipoprai SiaaTrjpaTaf al Si Kara 
Sid<f)(Opa» TOVTODP S* ai pip rjTTOP rj iKp^Xfis^ al Si pdXXop. 

ip oaais pip oZp avrSiP nXeicop fj Koiptopia^ ippiXiarepai* ip oaais Si 
iXaTTCDPf iKp€XiaT€pai* inciSrj dpayKodop natrrj pera^oXrj koipop ri 
vndpx^^Vy fj (l)d6yyoPy ^ Sidarrjpa, ff (Tvarrjpa, Xa/xjSdi/erai Si ff koi - 
pcDpia Ka0* opoioTTiTa (fidoyyodP, orap yap in dXXfjXovs ip rai? pera^ 
fioXais ninadnip opoioi (fidoyyoi Kara rfip rov ttvkpov p^rox^v, ipp^Xfjs 
yipfrai fj /xcrajSoX)}, orap Si dpopoioi, iKpeXrjs, * Modulations begin 
with modulation by the semitone, and proceed to the octave. 
Some of these are by concords and others by discords. Some 
of them are more melodious than otherwise; others less so. 
The greater or less the community of elements, the more or less 
melodious the modulation. For every modulation demands 
some common element, whether note, interval, or sfale. But 
this community is ascertained by the similarity of notes; for 
a modulation is melodious or unmelodious, according as the 
notes that coincide in pitch are similar or dissimilar as regards 
their participation in the Pycnum.* 



The last phrase of this passage requires some explanation. 
The Greeks considered that every note of every scale was 
actually or potentially the lowest, the middle, or the highest 
note of a Pycnum. Thus in the Enharmonic scale 

E is actually the lowest, XjE* actually the middle and F actually 
the highest note of the Pycnum E-xE-F. Similarly by xb and c 
are respectively the lowest, middle, and highest notes of the 
Pycnum b-xb-c. Similarly e is the lowest note of the Pycnum 
of the conjunct tetrachord by which we might extend the scale 
upwards. Finally Ay though not actually participating in any 
Pycnum in the above scale, does so potentially as the lowest 
note of the Pycnum A-xa^^by in the possible conjunct tetra¬ 


Representing the lowest, middle, and highest notes of a 
Pycnum by the signs LPy MPy and HPy we find these notes 
thus distributed in the Enharmonic scale : 


r 1} - --1- ! ■ ! -1—^- ■ 

K - 1 ' m 


The same terms naturally apply to the Chromatic Genus; 
and may be applied analogically to the notes of the Diatonic 
Scale: thus— 



This distinction in notes is a deep and essential one, in which 
the Svvafxis of the note is conceived in relation to the tetrachord 
in general, abstraction being made of the difference between 
the individual tetrachords. 

If then it be asked whether two scales admit of melodious 
intermodulation, the answer is *Yes, if they have a common 
element; and the more common elements they possess, the 
more melodious will be the modulation.* But when we speak 




of a common element, we mean not only certain points of pitch 
common to both scales, but certain coincident points of pitch 
occupied in both scales alike by lowest, by middle, or by highest 
notes of a Pycnum. In other words there must be a coincidence 
in pitch of notes of the same divafiis in relation to the tetra- 

Let us consider then in particular the possibilities of inter¬ 
modulation between the keys of the seven modes. 











1 — 


- J — 




4 - 





-i^j- * 

1^. j 










4 . ' 


A semitone separates the tonics of the Mixolydian and Lydian 


keys. Similarly related are the Dorian and Hypolydian. Taking 
the first pair as typical we find that although there are several 
coincident points of pitch in the two scales such as E and A, 
there is no common element, because these points are occupied 
in the two scales by notes of different Siva/ug in relation to the 
Pycnum, A for instance being LP in the Mhcolydian key, but 
MP in the Lydian. Hence between scales separated by a semi¬ 
tone there is no direct modulation. 

A tone separates the Lydian and Phrygian; the Phrygian 
and Dorian; the Hypolydian and Hypophrygian, the Hypo- 
phrygian and Hypodorian, Taking the first pair as typical we 
find that of the coincident points of pitch E, jfF, A, b, 
one alone, is occupied in the two scales by notes of the 
same Sivajiis, namely the lowest notes of a Pycnum. Hence a 
melodious modulation is possible between scales separated by 
a tone, though the common element is the smallest possible. 

A tone and a half separates the Mixolydian and Phrygian; 
the Phrygian and Hypolydian ; the Dorian and Hypophrygian. 
In such pairs we find no common element; and hence they do 
not admit of direct intermodulation. Two tones separate the 
Lydian and Dorian; and the Hypolydian and Hypodorian. 
Here again we find no common element, and no direct modu¬ 

Two tones and a half, or the Copcord of the Fourth, separate 
the Mixolydian and Dorian; the Lydian and Hypolydian; the 
Phrygian and Hypophrygian; the Dorian and Hypodorian. 
In the first pair we find several common elements Ey Fy Gy Ay e. 
In general, any two scales separated by a Fourth have many 
common elements, and modulation between them is highly 

Three tones separate the Mixolydian and Hypophrygian keys. 
Here we find no common elements. 

Three tones and a half, or the Concord of the Fifth, separate 
the Lydian and Hypophrygian; and the Phrygian and Hypo¬ 
dorian. In the first pair we find as common elements JG, Ay 
by c. Hence in general one may modulate most melodiously 
between scales separated by a Fifth. 

Four tones separate the Mixolydian and Hypophrygian. Here 



there are no common elements. Four tones and a half separate 
the Lydian and Hypodorian. Here again there are no common 

Five tones separate the Mixolydian and Hypodorian. Here 
we have E and e as common elements, and direct modulation 
is p ssible. 

The general result we arrive at is that when two scales are 
separated by a Fourth or Fifth, modulation between them is 
melodious in the highest degree; when they are separated by 
a tone or five tones, modulation between them is again melo¬ 
dious though in an inferior degree; but when they are separated 
by other intervals then these, melodious modulation cannot be 
effected between them directly, but only by the intervention of 
other keys. It follows that the limits of indirect modulation are 
strictly defined. Since direct modulation exists only between 
keys whose tonics are spaced by a tone, by a Fourth, by a Fifth, 
or by five tones, indirect modulation can only connect keys the 
space between whose tonics can be arrived at by addition and 
subtraction of these four intervals. But the only intervals that 
can result from the addition and subtraction of a tone, two tones 
and a half, three tones and a half, and five tones are the semi¬ 
tone and its multiples. Hence, if two keys have their tonics 
separated by any other intervals than these, modulation between 
them, direct or indirect, is impossible. See note on p. loi, 1 . i. 

Beside the /xeTajSoX^ ovarTifxaTiKri Bacchius (ed. Meibom, p. 13, 
1.26) mentions three other fi€Ta^o\ai affecting melody: y€viKr)y ‘ of 
genus ’; Kara rponovy * of mode ’; Kara ^609, ‘ of emotional char¬ 

1 . 6. I read rivos for MSS nvos. Xiyca di introduces an alter-, 
native statement, and the alternative statement of a question is 
a question. 

1 . 7- TToaa diaarrjfjLaTG, The answer to this question as 
appears from the last note is *four,* Kara ra (rifKjxiyva dtaaTrjfmTa^ 
Kii Kara tov tovov Kai Kara tovs n€VT€ tovovs. 

1. 10. fx€Xo7Touas. The other parts of Harmonic science have 
supplied the material of melody, notes, intervals, and scales; 
it remains for the composer to make a judicious use of it. The 
science of the use of musical material is the science of fzeXo- 


TToiui. One of the functions of this science will be to determine 
which class of melody is adapted to any particular subject; 
whether the energetic style suits the chorus of a drama, or the 
Hypodorian tragedy, or the Enharmonic lamentation. But 
this function manifestly lies beyond the limits of dpfiopiKrj. To 
this latter science, however, belongs the classification of the 
several melodic figures by which a composition takes its shape. 

In the Isagoge (ed. Meibom, p. 22, 1 . 3), we find the following 
account of this subject: MeXoiroiia eorl npoeiprj^ 

pipcDv pep&p appopLKrjs Kal \moK€ipipa)P Svpapip ^xoPTfop* St’ 
Sc piKonoita CTrtTcXctTai reaaapa cVtijz* ttKok^ Trcrrcta 

Topfj^ ayayrj [cp. above, p. I 2 I, 1 . 7] iarip fj did rSiV 

i^rjg <l)d6yy(op odds tov p^KovSy nXoKf) Sc fj ipaWd^ tS)p tc Siaoriy- 
pdrtop d4ais napaXXrjkoSy Trcrrcta Sc fj €<f>' 4pds tovov noXXaKis yiypo^ 
pivrj nXrj^iSf Toprj Sc fj cVt nXeiopa popfj Kara piav yivopivr] 

7rpo(l)opdp Trjs (fxop^s. 

^ Melopoeia is the employment of the above mentioned parts 
of Harmonic science which serve as a material to it. The 
figures through which Melopoeia takes final shape are four; 
the sequence, the zigzag, the repetition, and the prolongation. 

The Sequence is the progression of the melody through 
consecutive notes; the Zigzag, the irregular progression with 
alternate location of the intervals [i. e. every second interval 
is ascending, every second descending]; the Repetition, the 
constant iteration of one note; the Prolongation, the dwelling 
for a length of time on one utterance of the voice.’ 

*Ay<oyfj again is divided into three species (see Aristides Quint- 
ilianus, ed. Meibom, p. 29, 1 . ii), cWcia, or 17 did tS>p i^rjs (l)d6yy(op 
T^p €mTa(Tip TToiovpipr) (ascending by consecutive notes); di/a#ca/Lt- 
TTTov(Ta or f} did Tw €7Top4p<DP aTTOTcXovcra Trjp ^apvTrfTa (descending 
by consecutive notes); Trcpi^cp?}^ or fj Kard (rvprjppcpcup pci/ cVt- 
T€ipov(Ta, Kara di^^evypepoap Sc dpi€i(ra' rj ipaPTicos (ascending by 
conjunction and descending by disjunction, or vice versa). A 
more general definition of ttXoktj is supplied by Aristides Quint- 
ilianus (ed. Meibom, p. 19* 1 . 20), nXoK^ Sc, otc did tS)p kgO* uTrcp- 
fia(Tip Xap^apopepfop (Trotcopcda t^p p^Xwdiap)^ ‘the zigzag occurs 
when our melody proceeds by notes that have been taken with 
a skip between them.’ 



If we accept this more general definition of and regard 
the more particular definition given in the Isagoge as descriptive 
of one special case of the class, it is easy to see that every 
melody is capable of being analysed into these four figures as 
final elements. I subjoin a few examples of such analysis. 

(i) €v$€ia v€TT€(a ivoKatiTtrovaa 

dywy^ aycDyfj 

€vO€ta dvaK&ixirrovaa itXok^ 


dyoiyil €vO€ta ir^Trela 



rovfi TtXoidi avaK&fXTrrovaa irXoK^ 


irXoKi} evOeia 

dyeoyri ir€pL<p€pffS 





irXoicfi dyoryil euOeia 



■0 - 




ayojyf^ dyct)y^ 
evOeia dvaKdfxirrovaa 

1. 17 - In this sentence I insert iari after Se, read TrapaKoXovdeiv 
for napaKoXovd^l and insert d^Xov, 

Either this paragraph is defective in the MSS, or its brevity 
amounts to obscurity. Yet it is not wholly unintelligible as 
it stands. In the first sentence Aristoxenus asserts that to 
understand a musical composition means to follow the process 
of its melody with ear and intellect. We have already learned 
from Aristoxenus what parts these two faculties play. The ear 
detects the magnitudes of the intervals as they follow one 
another, and the intellect contemplates the functions of the 
notes in the system to which they belong. But the phrase 
^process of the melody’ turns the speculation of Aristoxenus 
into another channel. It reminds him of the difference that 
exists between music and such an art as architecture, the pro¬ 
ducts of which present themselves to our senses complete at 
one moment. Melody, on the contrary, like everything in 
music, is a process of becoming, in which one passes, and 
another comes to be ; and we require here memory as well as 
sense, to retain the past as well as to apprehend the present. 

But although this is undoubtedly the general sense of the 
passage, the logical connexion of the sentences is by no means 
obvious. 'Ev y€V€<T€i yap k.t.X. justifies the previous use of toI? 
yiyvop€voi9f but how is the sentence €k dvo yap tovtcov #c.t.X. 
related to what goes before ? The fact that the understanding 
of music requires memory as well as perception is a consequence 
rather than an explanation of the fact that melody is a process ; 
and rovrcav implies that aiadqai^ and pvrjprjy if not already 
mentioned, have at least been indicated. 

Of course the contrast between aKorj and didvoia [cp. p. 124 , 
1 . 17 ] must not be confused with the contrast between atadrjais 
and pvfjprj, 

P. 130,1. I. ct 84 Tip€£ iroiovvrai T4\rj #c.t.X. This paragraph 
contains a polemic against (a) the absurd theory that one who 



can notate a melody has reached the pinnacle of musical know¬ 
ledge ; and (6) the equally absurd theory, which, basing the law 
of harmony on the construction of clarinets, reduces musical 
science to the knowledge of instruments and their construc¬ 

1 . 6 . o\ov TLvo^ is governed by dirjixapTrjKOTosj ^ of one who has 
missed some whole ’ = ‘ missed something completely.* But 
perhaps we should read oXov, the accusative neuter used as 
an adverb in the same sense as the cognate accusative oXov 
dfidpTrjjia, and construe nvos in agreement with SirjpapTrjKOTos, 

1. 7 . Marquard, followed by Westphal, inserts an ov between 
oTi and Tvipa^y being ignorant apparently of the use of ohx^ on = 
oh pLovov oh, 

1. 13 . Marquard is wrong in bracketing ov yap dvayKalov icrri 
. . . eVn TO (l>pvyiov pL^Xos as a gloss. He does so on the sup¬ 
position that its presence in the text involves a petitio principii ; 
because, he would say, Aristoxenus proves his statement ‘ that 
the capacity to notate a melody does not necessarily imply the 
understanding of it * by an appeal to a parallel case in metrical 
science; and then proceeds to justify his analogy by assuming 
the truth of the statement. 

But Marquard has missed the course of the reasoning, which 
is as follows: You admit that to mark a metre is not the 
end-all of metrical science. On what grounds then ? Because 
it is a fact that a man may mark a metre, and yet not under¬ 
stand its nature. Very well then. The same fact holds good 
with regard to melodic science (as I shall prove hereafter); it is 
namely (yap) a fact that a man may notate a melody without 
understanding its nature. Therefore you are logically bound, 
to admit that to notate a melody is not the end-all of melodic 

1. 17 . This argument is based on two premises ; (i) Notation 
takes account of nothing beyond the bare magnitudes of intervals. 
( 2 ) Perception of the bare magnitude of intervals is no part of 
musical knowledge. 

In support of the first premiss he appeals to the following 
facts : 

(a) The notation makes no distinction of genus. Thus [see 


table 22 in Introduction A] the notes ^ ^ stand for the 


whether in the diatonic scale 

or in the chromatic scale 

though the interval in the first case is compound and diatonic, 
in the second case simple and chromatic. 

{6) The notation makes no distinction of Figure. Thus the 

(b Z . , . -fg- 

notes p ^ mark the interval of the sixth - 

both in the diatonic scale 

where its schema is tone, semitone, tone, tone, tone ; and in the 
diatonic scale 

' J- 

where its schema is tone, tone, tone, semitone, tone. 

(c) The notation makes no distinction of the higher and lower 

R C 

tetrachords of the scale. Thus the notes ^ ^ apply to the 


whether in the scale 



or in the scale 





yet in the first case the interval belongs to the tetrachord 
Mes6n, in the second to the tetrachord Hypat6n. 

The second premiss is evident from the undeniable fact that 
the perception of the distance between two sounds leaves all the 
vital distinctions of music untouched. 

1 . 25. To the reading adopted in the text Marquard w'ould 
object (i) that Aristoxenus never refers to the tetrachords Hyper- 
bolae6n and Hypaton; (2) that we know of no signs that were 
employed to denote tetrachords. But (i) in p. 99, 1 . 12 we have 
a reference to the Complete System of which the said tetrachords 
were parts; (2) when Aristoxenus speaks of the notation of a 
tetrachord, he means of course the notation of the notes of the 
tetrachord. The singular t <3 avrS arjixeicd is used because the 
sense is ‘ the same sign is used to represent a note of the tetra¬ 
chord Hypat6n and a note of the tetrachord Meson,’ &c. 

Marquard’s reading (given in the corrections at the beginning 
of his volume) to yap vfjrrjs Kai piicrrjs Ka\ to napapiiarjs Ka\ xmarqs 
has the fatal defect that these intervals are Fifths, not Fourths. 
Sense might be obtained by reading with Westphal to yap vrjTr^s 
Kai Trapapiearjs Ka\ to p^arjs Kai vnaTrjs, but this is rather far from 

the MSS. 

P. 131 , 1 . 6. ovT€ yap • . . yvoapipLov. An anacolouthon. 

1 . 10. TOV9 TO)!/ pLiKowouSiv TpdjTovs, See Aristides Quintilianus 
(ed. Meibom p. 29, 1 . 34), Tponoi Sc pLeXoirouas yivei /xci/ Tpciff* Siflo- 
pap^LKoSy vopiKos, TpayiKos. 6 pev ovu vopiKos Tponos cctI vrjToeLdfjs 
(i. e. its prevailing character is that of the tetrachord Neton), 
6 Sc didvpapPiKosy ps(TO€i8r]s (i. e. its prevailing character is that 
of the tetrachord Meson), 6 Sc TpayiKos vnaToeid^s (with the 
character of the tetrachord Hypaton). ctSci Sc evpiaKovrai nXeiovsy 
ovs bwarov 81 opoLorrjTa tols y^viKOis imo^dWeiv, cpcoTixo/ tc yap 
KaXovvrai TivcSy hv 18101 enidaXapioiy koI KcopiKoiy Kai iyKoapiaaTiKoL 
Tponoi Sc Xiyovrai 8ia to avv€p(l>aLV€iv nci)S to rjBos Kara to pcXi; Trjs 

1 . 21. Marquard, followed by Westphal, has made sad havoc 
of the following passage by changing the order of the sentences. 
In fact, the reading of the MSS calls for very little emend¬ 
ation. nipas must be inserted in 1 . 22 ; and I have omitted 
^ before tols in P. 132 , 1 . 3, and inserted Sc after it; and omitted 


V in 1 . 4, after nvevjia. No other changes are necessary, except 
in punctuation. The course of the argument is sufficiently clear 
from the translation. 

P. 132 , 1 . 12. fiiyiarov fiiv ovv. yikv ovv signifies a correction or 
strengthening of the preceding statement, ‘ No less absurd, nay 
rather most absurd of all.’ I have followed Marquard in reading 
aroTTOF though I am not at all sure that the addition is necessary. 
KaOoKov ixaKLOTa tSuv dixapTrjfmTODv might mean ‘ the most complete 
mistake possible.’ Cp. note on p. 130,1. 6. 

1 . 17. Koikias. The plural is very strange, if the word means, 
as it seems to mean, the main bore of the instrument. 

Mr. Howard {Harvard Studies in Class. Phil. Vol. IV, p. 12) 
quotes in support of this rendering Porphyrins ad Ptol. p. 217, 
ed. Wallis ; ndXiv de iav Xd^rjs 8vo avkovSf toIs jiiv firjKetTiv itrovSj 
Tots 8e evpvTTjai t 5 )v KoikiSiV 8La(f)€povras* Kaddnep exovaiv 01 ^pvyioi 
TTpos Tovs ^^WrjpiKovs' €vprj(T€is Tvapankr^dioas to evpvKoiKiov o^vrepop 
TTpoupevop (f)d6yyop tov arcvoKoiXiov* deoapovpep yk toi tovs ^pvyiovs 
arkvovs rais KoiXiais ovras km ttoXX© ^apvrkpovs rj^ovs npo^dXXovras 
rOiv"^XXrivLKfdv, AlsoNicomachus(ed.Meibom,p.8,].33),dm7raX£i/ 

06 rSiv ipirv^vfTTGiv ai pei^oves KoiXionaeis koI tcl pei^opa pijKT], payOpop 
Kai ckXvtop. He cites too the parallel use of the Latin cavernae 
by Servius ad Aen. ix, 615. 

If it were not for the strength of these passages, one might 
suppose KoiXias here to refer to the sidetubes with which some 
avXoi were furnished, and which served, when in use, to lower 
the pitch of the instrument (see Mr. Howard’s article, p. 8). 

1 .18. Marquard inserts 6 avXrjrfjs unnecessarily. He assumes 
that oh in 1. 19 must be an instrumental dative, and that 
must be used personally, in which case the construction will be 
6 avXbs 7rk(l>VK€p imreip^ip Kai dvikpai,, and kniTcipeiP and dpikpai will 
be used intransitively. But there is no reason why oh may not 
be a dative after 7rk(l>vK€p = [those other parts] to which it is 
natural [to raise and lower tone]. 

1 . 24. ravra, Cp. p. 122, 1 . lO. 

1 .25. Ka\ yap d(f)aipovpT€9. For the violent ellipse by which ydp 
is left without a finite verb, cp. p. 145,1. 6, ^ yap (rvp^fxopiiv. 

Should we read Trapatpovvrfs for d<f>aipovvT€s ? For this 
expedient of bringing the two pipes together, and drawing 




them apart, and for its effect on the pitch, see the last clause of 
the sentence from Plutarch (non posse suaviter 1096 a) quoted in 
the note on p. 112,1. 15. 

P. 133 , 1 . 2. ovhkv bia(f>€peL 'keyeiv k.t.X. Here Marquard’s 
translation is distinctly amusing, ‘daher macht es offenbar 
keinen Unterschied, ob man sagt ‘‘ gut die Floten ” oder 
^‘schlecht.”’ Westphal is equally ridiculous: ‘ sodass es meistens 
eigentlich dasselbe besagen will, wenn das Publikum beim 
Aulosspiel ‘‘ gut ” oder ‘‘ schlecht ” ruft.’ The meaning simply 
is that the goodness or badness of the music does not depend 
upon the instrument. 

1 . 21. davfiaarbv S' el k.t.X. One more argument. Clarinets 
are changeable instruments, and their music must alter with the 
alteration in themselves. 

P. 134 , 1 . 5« The MSS to elpr^pevov opyavov cannot be right. 
The argument plainly is (l) instruments in general will not 
serve as bases for the laws of harmony; and (2) least of all will 
that very defective instrument, the clarinet, do so. For Spyavov 
used alone cp. p. 133,1. 4. 

1 . 14. np^Tov pev avTOiP k.t.X. It is required of us firstly to 
ascertain the phenomena correctly, secondly, to distinguish 
truly in these phenomena what is primary and what is derived, 
thirdly to grasp aright the result and conclusion. In other 
words we must first observe accurately, then analyse our facts 
and find the essentials, then sum the results of our observation 
and analysis in a generalization. The generalizations, which 
we shall thus obtain, will be the dpxai^ or fundamental principles 
of our science, from which its other propositions will be deduced. 
It is indispensable that such fundamental principles should be 
(a) indisputably true; (d) recognizable by our sense perception 
as primary truths of music. 

The science of Harmonic then as conceived by Aristoxenus 
starts from the observation of individual facts, and proceeds by 
induction to general principles, which serve in turn as foundations 
for a train of deductive reasoning. 

1 . 17. 70 V (Tvp^aivopTos . . . avpocfydePTos. This passage is mis¬ 
translated by Marquard ‘die methodische Beobachtung des 
Zufalligen und Uebereinstimmenden,’ that is ‘ the methodical 


observation of the contingent and constant ’; by Westphal ‘ so 
muss der Sache gemass erkannt werden was sich (erst) als 
Schlussfolge ergiebt, und was in die Kategorie des allgemein An- 
genommenen gehort/that is, ^we must distinguish in accordance 
with the facts what is only arrived at as a conclusion, and what 
belongs to the category of the universally admitted/ But (i) to 
(Tvfi^alvov and TO dfio\oyovfi€vov are technical terms for the result 
and conclusion; (2) awopav means ‘to see the connexion of things’ 
not to ‘see the difference’ between them ; (3) if to (rvp^aipov and 
TO ofioXoyovfievov are distinct and contrasted classes, we should 
require tov (rvfi^alvovTOS koX tov ofxoXoyovfJLcvov. 

1 . 25. KadoXov S’ iv tS k.t.X. We must neither trace back our 
musical phenomena to physical and non-musical principles; 
nor be content till we have resolved them into the ultimate laws 
of music. 

1. 27. For rj of the MSS I read 17 in the sense of gua ‘re¬ 
garded as.’ 

P. 135 , 1 . 1 . KafXTTTovres ipros. A metaphor from the race-course. 

1 . 7* V , fi Koipop. See Isagoge [ed. Meibom, p. 9 j 

1 . 34 ]j koipop Sc to €#c tSup €(tt&t(op avyKcifiepop, fxiKTOP Sc to cV 

8vo fj Tpcls yepiKol €p,(f)aipojrrai. A melody is common 

when it employs only the fixed notes, which, of course, are 
common to all three genera ; it is mixed, when it employs notes 
of different genus. 

1 . 12. TT^puxerai S’ ^ vdripa . . . n pore pa. That is the differ¬ 
ence between concords and discords in one special case of the 
difference between larger and smaller intervals. The conno¬ 
tation of the 8ia(j)opd between concords and discords contains 
the connotation of the 8ia(j>opd of size, but the denotation of the 
Siacpopd of size contains the denotation of the 8ia<f>opd between 
concords and discords. 

1 . 18. The MSS are corrupt here. It is absurd to say that 
the Fourth is determined as the smallest interval by its own 
nature. It is so determined by the nature of melody or song, 
inasmuch as all the smaller intervals which the latter produces 
are discords. The correction is due to Westphal. 

P. 136 , 1 . I. ravra /lev ovv \eyo[t€v & napa tS>p epirpoadev Trapet- 
\f)<^ap€v. Marquard rejects this sentence on the ground that 


T 2 


the sense required is not ‘ we say what we have learned,’ but 
‘what we say, we have learned.’ But, just as ravra Xiyofxev 
dXrjdri means ‘in saying this we are speaking the truth’ (the 
predicative force lying in the dXrjOri), so here the meaning is 
‘ in the above statements we are repeating what we have learned 
from our predecessors.’ 

1 . 6. ndSos. Cp. the use of Tvd(TX<^ in p. 145, 1 . 17 ; p. 156, 

1. 5 ! p* i59j 

1. 10. ovr€ TO iKarepov k.tX. Meibom, Marquard and 
Westphal alike find this sentence unintelligible. Is it not 
a fact, they ask, that the sum of a Fourth or Fifth and an 
octave is a concord? Accordingly they correct the reading 
by inserting Sis redevros after iKarepov avrSiv. But the MSS are 
perfectly right, and the commentators construed wrongly. 
Written in full with the ellipse supplied, the whole sentence 
runs, ovT€ yap TO laov cKOTepco avTd)v awredev to oXov (rvpcjxopop 
TTOie?, ovT€ TO eKOTepov avTciiv Kai toO 8id nacrSyu <TvyKeipL€vov 
cKaTepfo avTOiv awTeOev to dXov (r{fpi(poi>pop TroieZ, and the meaning 
is ‘Add to a Fourth or a Fifth an interval equal to itself; the 
result is a discord. Add to a Fourth or Fifth respectively 
the sum of an Octave and a Fourth or Fifth; again the result 
is a discord.’ 

According to the absurd misconstruction of Meibom, Marquard 
and Westphal, the second part of the sentence in its complete¬ 
ness is as follows : ovtc to cKOTepov aiTS)p 8\s TcdePTOs Kai tov 
8id naadip avyKcipcpop to oXop (TvpL(l)oi)vop noiei. Now it is quite 
correct to say ‘4 added to 6 causes the whole to be 10’ or 
‘ the addition of 4 to 6 causes the whole to be 10,’ but surely 
not to say ‘ the sum of 6 and 4 causes the whole to be 10.’ 

1 . 18. Aristoxenus introduces two warnings. When he says 
that it is possible to sing the third or fourth part of a tone, he 
must not be misunderstood as saying that one can in singing 
divide a tone into three or four parts. For that would imply 
the possibility of singing three thirds of tones or four quarter- 
tones in succession which is against one of the fundamental 
laws of melody [see p. 119,1. 20]. 

Again, he has mentioned no smaller division of the tone than 
the quarter-tone, because the voice can sing and the ear dis- 


criminate none smaller. But it must not be forgotten that in 
the abstract there cannot be a minimum interval any more than 
a minimum space or time. 

P. 137 , 1 . 4. 6 t€ §€ darepov Between the Diatonic and 

Chromatic scales there is only variation of the Lichanus, as 
these genera have their Parhypatae in common. 

P. 137 , 1 . 18-P. 138 , 1 . 6. Marquard is greatly disconcerted 
by the abrupt transitions which he finds in this passage from the 
indicative to the accusative and infinitive construction. Besides 
correcting rightly Sri to Seiv in p. 138, L 3, he omits ean in 
p. 137, 1 . 20 to remove the incongruity. As a fact, with the 
exception of the blunder Sri for Srii/, the reading of the MSS is 
quite unexceptionable, and the construction normal. The quoted 
questions are in the indicative, the quoted state 7 nents in the 
accusative and infinitive. The ^ivai that follows Bcriov in p. 137, 
1. 23 is grammatically dependent on it, and not the infinitive of 
oratio obliqua^ as Marquard supposes. 

1 . 18. The objection cited in this paragraph, and the answer 
of Aristoxenus to it, raise again the conflict between the super¬ 
ficial view of notes as points of pitch, separated by certain spaces, 
and the deeper view of Aristoxenus according to which notes 
are essentially members of a system with special functions. The 
objection is stated in 1 . i8-p. 138 , 1 . 5 and here again Marquard 
has quite wantonly perverted the order of the sentences. The 
argument of the objection may be stated thus: ‘ We object to 
applying one term, say the term Lichanus, to several points of 
pitch at different distances from the Mese. The term Hypate 
signifies one certain point at one certain distance from the 
Mese; why not similarly restrict the term Lichanus to some 
one point, say the point two tones below the Mese, your 
Enharmonic Lichanus; and use other names for what you 
call the Chromatic and Diatonic Lichani? For we hold that 
notes which bound unequal magnitudes must be different notes; 
or, to put it more plainly, that a difference in the size of the 
contained interval necessarily implies a difference in the con¬ 
taining notes. We hold equally, by simple conversion of this 
proposition, that different notes must bound different intervals, 
or that a difference in the containing notes necessarily implies 



a difference in the size of the contained intervals. Consequently 
a proper nomenclature will always employ the same terms to 
denote the points bounding the same magnitudes of intervals ; 
and will always employ different terms when the bounded 
intervals are unequal.’ 

1 . 19. Marquard reads reOivTos for Kivr^devros on the ground 
that it is when one posits, not when one changes, one of the 
possible intervals between the Lichanus and Mese that a 
Lichanus results. But the sense is rather this: The objectors 
urge that between any two notes there must be but one interval; 
if this interval be changed^ then there must, say they, be a change 
of notes also. 

P. 138 , 1 . 2. The addition of \ixav6s is perhaps unnecessary; 
KXrjdrj might stand by itself for ‘ receives the name.’ 

1 . 3. Probably S is right in omitting to. 

1 . 5 * The sentence ra yap taa rSav to is avrois ovopatTi 

TTcpiXrjTrTeov elvai is the simple converse in sense, though not 
in form, of deiv yap irepovs elvai (f>d6yyovs Toifs to cTCpov pL€y€dos 
opiCovTas. For the former sentence =‘ equal intervals should be 
bounded by identically-named notes’ = ‘no notes should have 
different names unless they bound unequal intervals’= ‘no notes 
are really different unless they bound unequal intervals’=‘all 
different notes bound unequal intervals,’ which is the simple 
converse of ‘ all notes that bound unequal intervals are different 

1 . 9. Before dealing with the original proposition of the ob¬ 
jectors Aristoxenus disposes of its converse by insisting that 
the essential feature of a note is its divapis^ and that nomen¬ 
clature cannot overlook the distinction between the notes a and 
e in the scale 

when they are Mese and Nete, and the notes a and e in the 

when they are Lichanus and Paranete. 


1 . 14. I read ci', to for iv rwof the MSS. 

1. 16 . oTt 8 * oiSc TovvavTLov k.t.X. Having disposed of the 
converse Aristoxenus turns to the original proposition, which 
requires a special refutation; for the two propositions are 
related to one another as a Universal Affirmative and its simple 
converse; and the falsity of one does not prove the falsity of 
the other. Aristoxenus has to prove not only that inequality 
in the contained intervals is not the sole ground for distinguishing 
notes by name, but also that it is no sufficient ground for doing 
so at all. His arguments are two: 

‘ In the first place, if you insist on having different names 
wherever there is a difference of interval, you will require an 
infinite vocabulary. The voice, for example, may make its second 
resting place in the passage of the tetrachord at any point between 
a semitone above the Hypate and a tone below the Mese. The 
number of such points is infinite. We call them all Lichanus, 
but you who insist that a difference of interval demands a differ¬ 
ence of name will require an infinity of names. Perhaps you 
will think that this is the quibble of a casuist; that as a matter 
of fact three terms would do, one for the Enharmonic Lichanus, 
one for the Chromatic, and one for the Diatonic. But it is no 
quibble. For consider seriously (iy oKriOSis): different schools 
or theorists assign different positions to the Lichani of the 
different genera; and there is no earthly reason for giving one’s 
adherence to one of these schools rather than another. Take 
a special case. Some theorists locate the Enharmonic Lichanus 
at two tones below the Mese; some place it a little higher. 
Supposing, then, that we even went so far with you as to restrict 
the term Lichanus to the Enharmonic Lichanus, we should have 
just the same difficulty again. For here are two upper passing 
notes, one two tones below the Mese, and one a little higher; 
both of them to the ear give an Enharmonic scale, so that both 
have equal claims to the name of Lichanus: yet they bound 
unequal intervals from the Mese, therefore, on your theory, the 
one name will not apply to both.’ 

‘ In the second place, your demand ignores the fundamental 
character of sense perception which, abstracting from the petty 
distinctions of quantity, looks to the similarity of things through 



their possession of common qualities. Thus the juxtaposition 
of two small intervals produces on the ear an impression of 
a certain sort^ which remains the same whatever the exact size 
of the intervals may be ; and one uses the genera! term Pycnum 
for this juxtaposition. But on your principle, one has no right 
to employ this term, since Pycna are of different sizes. Similarly, 
one has no right to speak of Enharmonic, or Chromatic, or 
Diatonic, for all these classes imply the ignoring of mathematical 
differences. If, on the other hand, we do admit a class Pycnum, 
a class Enharmonic, why not also a class Parhypate and a class 
Lichanus ? Fot just as in the case of Pycna you have a general 
feature, namely, a certain compression, and as in each genus 
you have a certain character common to the particular cases of 
it, so here you have as common features the species or figure 
of the tetrachord, that is, a plan of four notes, the two outer 
fixed at an interval of a Fourth with the upper as tonic, and two 
passing notes between them.’ 

1 .17» F or aKo\ovdrjT€ov of the MSS I read aKoXovdeiv 6 ^t€ov, The 
preceding sentence asserts that A is not a necessary result of B ; 
nor, continues Aristoxenus, must we allow that B is a necessary 
result of A. But clkoXovO^Iv cannot mean ‘ to assert a necessary 

TovvavTiov cLKoXovO^Lv = ‘ the opposite order of dependence.’ 

1 . 21. 0)9 aXrjdoiS . . . fV €KaT€pa tS)v diaipecreiov* I have 
transposed this passage from its unintelligible j>osition after 
8iap,€v€iv in p. 140, 1 . I. In its proper place it is most serviceable 
in answering the certain objection that to talk of an infinity of 
Lichani is mere casuistry. 

P. 139 , 1 . 2. It is quite unnecessary to insert with Marquard 
and Westphal oi naw paSiov (rwiSelv, fiorf may very well 
introduce a conclusion pressed against an adversary in the form 
of a question. 

1. 13. Xcyo) Sf is parenthetical, and ndelaa agrees with eKelpif 
and stands in apposition to els opoioTrjTa . . . 

1 . 14. I read fQ )9 for 0)9 in 1 . 14, and Sf fi 8 o 9 €(os av for hi ^ 
di6(r€a)9 av in 1 . 17. For €q) 9 in the sense of ‘ to cover all cases in 
which’ cp. p. 141, 1 . I. 

1 . 16. nvKvov Tivos (fxovrj. If the reading is correct, ttvkvov 


Tivos must be construed as a genitive of the material; ‘ a voice- 
utterance consisting in a compression/ i. e. in a succession of 
close-lying notes. 

1 . 21. I insert /xeVfii/ after (rvix^aivei, 

P. 140 , 1 . 9. Finally, Aristoxenus shows a palpable absurdity 
that would result from the acceptance of this principle—the 
absurdity of one note bearing more names than one in the same 
scale. In the first place let us take two equal intervals in 
succession; for instance, the interval between e and /, and 

between / and 5 /in the Chromatic scale 

X Y 

If we insist on using the terms X and Y universally for the 
lower and higher notes of an interval of this size, the f of the 
above scale will be both X and Y. 

In the second place, let us take two unequal intervals, the 
interval between e and/and that between/and ^ in the Diatonic 


M N 

On the principle under exami 

nation, inasmuch as the names signify no function or intrin¬ 
sic qualities of notes, but merely a space relation between 
two points whose only quality is that they are so far from one 
another, every such name of a point must connote its relation to 
another point at some certain distance; and cannot be employed 
outside this relation. Thus every change in the size of an 
interval will demand a new pair of note-names. Hence in the 
present case the intervals between e and / and between / and 
g will bear two distinct pairs of names, say XY and MN; and 
/will bear two names, Y and M. 

P. 141 , 1 . I. In this paragraph we have another exposition of 
the genera and their ‘ shades.’ See pp. 116-118. 

P. 142 , 1 . 23. The missing words have been well supplied by 

P. 143 , 1 .13. I have little doubt that we should read XcKreov for 
heiKriov. Cp. p. 147, 1 .25, where all the MSS read Xeicreop instead 
of the plainly necessary 8 €ikt€op. 



1 . 18. ayayyrjs: cp. p. 121, 1 . 7. The term is here used, not of 
a particular melodic figure, but of the general consecution of 

1 . 19. I omit the words ov yap 8ia toctovtodv Swrjdeiri tis av as 
a gloss which has crept into the text. They are meaningless 
by themselves, and require the addition of p€\<o8elvy or the 
like; even when thus emended they present a singularly weak, 
and at the same time wholly unnecessary statement. The gloss 
was occasioned by the ambiguity of the following pexpi>* 

1 . 20. here = ‘ up to, but excluding.’ It more often means 
^up to and including’ (see p. 131, 1 . 3). The same ambiguity 
attaches to €Q)9. Cp. p. 144, 1 . i, and p. 140, 1 . 4. Perhaps, 
however, we should read adwarel here. 

1 . 21. TO i^rjs oijT iv k.tX. The nature of melody brings it to 
pass that (a) sometimes the next note to a given note is separated 
from it by the smallest possible interval, as in the Enharmonic 


the next note above xe is /. 

(6) Sometimes the next note to a given note is separated from 
it by an interval of considerable size, as for instance in the same 
scale the next note above / is a. (c) Sometimes a consecutive 
progression moves by equal intervals as from / to ^ in the 

Diatonic scale 


(d) Sometimes 

a consecutive progression moves by unequal intervals as from 

f to b in the Chromatic scale 

Consequently, the true conception of continuity is not derived 
from the notions of the minimum, the equality, or the inequality 
of intervals. 

P. 144 , 11 . 8-9. Affer much hesitation I have accepted Mar- 
quard’s reading, though I believe his interpretation of it to be 
quite erroneous. The difficulty lies in the genitive tov Trpofipiy- 
pevov apiBpov : the general argument is clear. If we admit that 


the maximum number by which the distance AB can be divided 
is four 

X y z 

A -!-^^- B 

it is evident that the points A^ x^ y, Zy B are consecutive, and 
admit of no intermediate points of section. Aristoxenus refers 
to these points A, x^y^ z, B as 4 he notes that bound fractions 
of the said number.’ Marquard identifies the number with the 
distance ABj and regards tov Trpociprjfieuov apidpov as a partitive 
genitive. But, to take the above illustration, dpidpov evidently 
refers not to the distance AB but to the number four by which 
it has been divided. For it would not be true to say that the 
points which bound parts of the said interval are consecutive; 
Ayyy B for example bound parts of it, and are not consecutive. 

We must therefore understand the partitive genitive tov 
S iaar^paros with pcprjy and interpret tov irpoeipripLcvov dpidpov as 
‘having the said number as denominator.* To recur again to 
our illustration, the whole phrase tov npo€ipT]p€Pov apidpov p^prj 
Tou Siao-T^/xaroff would mean ‘fractions-of-four’ (or ‘fourths’) ‘of 
the distance ABJ 

1 . i8. I read \ap^av€T(o for Xap^avcTai of the MSS, as the 
middle voice is out of place. XapL^aveTco is parallel to iKpLeXrjs 
eoTQ) that immediately follows. 

Meibom wished to read prjdeTepov for prjd^Tcpa. But Marquard 
points ouf that each alternative here referred to comprehends 
two relations, those of any given note to a certain note above 
it and to a certain note below it. 

1 . 20. ov Sci S* dyvoelv k.t.X. For instance, the scale 

obeys the above law; yet it is illegitimate, because it violates 
the law of the tetrachord that the interval between the lower 
fixed note and the first passing note must never be greater than 
that between the two passing notes. 

P. 145 , 1 . 5. Set yap tois k.t.X. The law of the sequence of 
tetrachords is as follows: two tetrachords belong to the one 
scale either if the notes of one form some one concord with the 



corresponding notes of the other, or if the notes of both form 
a concord with the corresponding notes of a third tetrachord 
of which they are both alike continuations, but in opposite direc¬ 
tions, one upwards, one downwards. 

Thus, in the Greater Complete System (see Introduction A, 

§ 29) 

the notes of any one tetrachord form some one concord (Fourth 
or Fifth or Octave) with the corresponding notes of any 

Again, in the Lesser Complete System (see Introduction A, 

§29) c - 

Mes6n Synemmenon 


j -i 

the corresponding notes of the Hypat6n and Meson tetrachords 
form Fourths with one another; as do also the corresponding 
notes of the Meson and Synemmenon tetrachords. But what 
about the Hypaton and Synemmen6n tetrachords? They 
evidently belong to the one scale, and yet the notes of one 
do not form a concord with the corresponding notes of the 
other. Here the second clause of the law applies. The 
Hypaton and Synemmenon tetrachords are both continuous 
with the Meson, but in different directions (/x^ cm rbv avrov 
TOTTov), one lying below it and one above, and the notes of the 
Hypatbn and Synemmenon form concords with the correspond¬ 
ing notes of the Mes6n. 

1 . 9. Marquard, followed by Westphal, wrongly altered t6v 
avTop Tonov to tw avrw tottq), and supposing it to refer to the 
coincidence of the extremities of conjunct tetrachords proposed 
to omit the fifj of 1. 8. 

1 . II. It is uncertain what are the other conditions of the 
legitimate synthesis of tetrachords, to which Aristoxenus here 


alludes. One may perhaps have been a certain order in the 
employment of conjunction and disjunction. Thus the scale 

might be regarded as illegitimate, because the conjunction and 
disjunction do not occur alternately. 

1 . I5» The MSS here read aXX’ iv jieyidei &piaTai, which I have 
corrected to aXX’m ficyedei iipiadai. capiadai is the infinitive after 
fio/cel, and with navreX^s aKapiaiov riva one repeats 8ok€i tottop, 
Marquard reads ovk €)(€ip SokcI tottop aKXJ fj el peyedei &pL(rTai^ rj 
TTavT€\S>s cLKapiaiop riva and translates absurdly ‘ seem only to take 
place when they are determined in magnitude, or at any rate 
only in a highly limited degree.* Of course tottop means 
‘ to have a locus of variation.* The same misconception under¬ 
lies Westphal’s reading ovk exeip doKel fj Trai/TcX©^ aKapialop Tiva 
TOTTOP dXX* ff el TCL pLeyedr] &pL(rTai, 

1 . 19. oKpi^eaTaTTf k.t.X. Note Aristoxenus’ recognition of 
the truth that the determination of all intervals must in the 
last resort fall back upon the elementary relations of the 

8’, deleted by Marquard, may be an example of the 8 e ottoSo- 


1 . 22. Ta)p dvvaT&v. Intervals smaller than semitones cannot be 
determined by concords. For the Fourth consists of two and 
a half tones, the Fifth of three and a half tones, and the Octave 
of six tones; and no repetition, addition, or subtraction of these 
numbers will lead to any fraction smaller than a half. 

1 . 23. €TTi TO K.T.X. If it be required to ascertain by concords 
the note that lies two tones below G, the following will be the 




The note that lies two tones above G is ascertained thus : 

P. 146 , 1 . 5. yiyverai de #cai k.tX This is evident. If in the 


n ^ -I , ■ — 

we determine the ditone between 

a and f by concords we have in so doing also determined by 
concords the semitone between e and/ For ^ is given in concord 
with and f has now been determined by concord with a ; 
and e and /are the bounding notes of the semitone. 

1 . 20. noTcpop 8’ 6p6S)s k.tX The following is Aristoxenus’ 
demonstration that a Fourth consists of two tones and a half 
(a tone being the excess of the Fifth over the Fourth). Take 

a Fourth e-a, and determine by concords the note / two tones 
below a, and the note two tones above e. It follows that the 
remainder ^-/=the remainder because each of them=the 
whole Fourth, e-a, less by two tones. Now take the Fourth 
above/namely and the Fourth below namely There 
will now lie side by side at each extremity of the scale two 
remainders, which must be equal for the reason already given ; 
that is, and a-%a are all equal, because each of 

them equals a Fourth less by two tones. 

Now if %d and the lowest and highest notes of the scale, 
be sounded, our ears will assure us that they form a concord. 
This concord, as greater than a Fourth by construction and 
obviously less than an octave, must be a Fifth. But since 
%d-%a is thus found to be a Fifth, and %d-%g by construction 
is a Fourth, must be the difference between a Fourth 



and a Fifth; in other words, a tone. But we have already seen 
that jf£--a=a-jfa semitone. But by the construction 

^-#^=two tones; therefore e-a being the sum of e-%g and %g-a 
must be equal to two tones and a semitone. 

P. 147 , 1 . 4* The MSS read 8vo etrovrai koI fitj tv al 

V7r€poxai which Marquard and Westphal following Meibom correct 
by changing ^v to pia. But (i) how did the grammatically 
obvious fxia come to be corrupted to €v ? (2) what is the sense of, 
insisting that the remainders are ^ not one ’ ? (3) the article before 
vmpoxai is objectionable, as the meaning is ^ there will be two 
remainders.’ I read KcipLevat for koI tv ai. Kcip^vai avvex^ls^ 

‘ lying side by side,’ ^ in juxtaposition.’ 

1 . 9. The absurd rirrapa in this line and in 1 .15 arose of course 
from the scribe mistaking the S of h^ov and the S’ before o^vrarov 
for numerals. 

P. 148 , 1 . I. The MSS read Sitovov* avyx<»>p€iTai napa navTcav 
IC.T.X. Marquard followed by Westphal inserts dXXa before 
a‘vyx<»>p€iTai ; but I prefer (Tvyx<»>p€iTai yap, because (i) the sentence 
supplies a reason, (2) yap might easily have been lost before Trapd. 

P. 149 , 1 . 12. Before we consider Aristoxenus’ exposition of 
the continuity of tetrachords, there are two points to be noticed. 
Firstly, whereas in his former sketch of the matter [p. 145, 11 .3-13] 
he considered the relation of similar tetrachords only, here his 
treatment takes into account the differences of Figure. Secondly 
there is an ambiguity in the terms avvexrjs and which some¬ 
times signify merely ‘in the same line of succession,’ at other 
times ‘ nexl in the line of succession.’ 

In general, Aristoxenus asserts, tetrachords are in the same 
line of succession if their boundaries are in the same line of 
succession or coincide. In this general definition are explicitly 
given the two species of succession of which tetrachords are 
capable. We have a case of the one species when the lower 
boundary of the higher of two tetrachords coincides with the 
upper boundary of the lower; a case of the other species, when 
the lower boundary of the higher of two tetrachords is in the one 
line of succession with the upper boundary of the lower. 

Now we must not confuse this distinction with the distinction 
between conjunct and disjunct tetrachords. The latter distinction 



divides successive tetrachords into (a) those whose extremities 
coincide; and (d) those whose extremities are divided by one 
tone. The former distinction divides successive tetrachords 
into (x) those whose extremities coincide; and (y) those whose 
extremities are in the same line of succession. Now the class 

(<^) = the class (x), but (d) is only one subdivision of the class (y). 
Thus in the legitimate scale 

the tetrachords E-F-G-A and c-d-^e-f fall into the class (j/), 
since A and c are in the same line of succession, but not into the 
class (^), since they are separated not by one tone but by a tone 
and a half. 

Now if two tetrachords belong to the class {a) (and con¬ 
sequently to (x) also) they must be similar in figure. Otherwise 
as in the pair 

we shall find a violation of the fundamental law of continuity 

[p. 120, 1. 16]. 

On the other hand, if tetrachords belong to the class (y) 
they will sometimes be similar, sometimes dissimilar in figure: 
similar, when they belong to the class (^), that is when their 
extremities are divided by a tone (and also, of course, if they are 
separated by a full concord); dissimilar, if they are separated by 
any other interval. 

Thus in the scales 


E-F-G-A and E-F-G-A and in the 

first, and E-F-G-A and C-D-e-f E-F-G-A and f-g-a-b^ 
E-F-G-A and B-C-D-e in the second are all examples of 
class {y) ; but only the last pair are examples of class (b) and 
only the last are similar in figure. 

Since then we have seen that all successive tetrachords may 
be divided into (x) and (_y), and since all (a) are (x) and are 
similar in figure and only those (y) are similar which are also 
(b)y it follows that all similar tetrachords in the same line of 
succession are either (a) or (b). As Aristoxenus says, ra 
T€Tpdxop8a opoia ovra rj (rvvr)pp4va avayKoiov elvai ^ Sie^evypeva, 

P. 140 , 1 . 14. In general, tetrachords in the same line of 
succession cannot be separated by a tetrachord dissimilar to 
themselves; for 

I. Similar tetrachords in the same line of succession cannot 
be separated by a tetrachord dissimilar to themselves. 

For if it be possible, between the similar tetrachords E-F-G-A 
and d-]^e-/-glet the dissimilar tetrachord A-B-jj^C-dhe inter¬ 

The resulting scale is illegitimate, because f neither forms a 
Fourth with the fourth note below it, nor a Fifth with the fifth. 

2. Dissimilar tetrachords in the same line of succession cannot 
be separated by a tetrachord of any figure. 

For if it be possible, let the two dissimilar tetrachords 
E-xE-F-A and jt/“^be in the same line of succession 

and separated by a tetrachord of any of the three figures. 






Any one of the resulting scales is illegitimate. In (a) for example 
xA neither forms a Fifth with the fifth note above it nor a Fourth 
with the fourth; and the other scales suffer from the same 

P. 151 , 1. 4. For ov €(TTi I read o y carl for two reasons. Firstly, 
the sentence is thus made exactly parallel to the next; and 
Aristoxenus is fond of such parallelism. Secondly, if we read 
01/, the meaning is ^ People take the ditone as simple and then 
wonder how it can be divided ’; but we require rather ^ People 
know that the ditone can be divided, and then wonder how it 
can be simple ’; and this sense is secured by reading o y iari 
The difficulty which Aristoxenus here resolves arose from the 
common misconception by which one decides an interval to 
be simple or compound by its dimension, without taking into 
account the scale to which it belongs, and the functions of its 
containing notes. 

1 . 17- I omit TO 8’ idiov TTfs aKivrjTOv iariv. The fact 

that the disjunctive interval (the tone) does not vary is used 
to prove the theorem, and therefore cannot be part of the 
statement of it. 

1 . 22. The disjunctive interval is constant because the notes 
that contain it are fixed notes. 

P. 152 , 1 . 14. For MSS davvOera irXcicFTa I read da^vvOera ra 
TrXcio-ra. Cp. p. 153, 1 . I. 

1 . 18. For the MSS efinpoadep redelaa Marquard and West- 
phal read TTpoandeicra, supposing the epiirpoadev to have crept 
in from 1 . 16. I read ep npoandeicra ; €P helps to account for the 
corruption, and strengthens the expression of the argument. 

P. 153 , 1 . II. 5 ti Kai iXaTTOPayp k.t.X. Defective or 
transilient scales [see Introduction A, § 26] contain fewer 
intervals than the simple parts of the Fourth. Also in the 
Enharmonic scale of Olympus [see note on p. 115, 1 . 2] the 
Fourth was only divided into two intervals. 

1 . 13. TTVKPop Sc TTpoff TvvKPtp K.T.X. The next eleven pages 
are occupied by a series of special rules as to the succession 
of notes and intervals, all of which rules derive themselves 
immediately from two fundamental laws. One of these laws, 
that by which the order of intervals of the original tetrachord is 


determined, is always presupposed by Aristoxenus; the other 
which demands a Fourth between fourth notes or a Fifth between 
fifth notes [see p. 120, 1 .16] is explicitly quoted. To understand then 
all these special rules, it is only necessary to keep before one’s 
mind (a) the form of the original tetrachord, and the functions of 

its notes as regards the Pycnum 

note on p. 129,1. 4] and (6) the possibility of choosing between 
conjunction and disjunction both in the ascending scale 

and in the descending scale 



P. 156 , 1 . 5. I read with M Tolpavriov Trenopdev dn\S)S ov 8vpd^ 
fxeva. The Other M SS have 8 vpdfi€da for dvpdfieva which Meibom 
retains, inserting a before drrXios. Marquard, rightly urging 
that the explanation of the general phrase Tovpapriop n€7ropd€v 
would not be given in a relative sentence, reads Tovpapriov 
nenopde Ka\ a7r\d)s, and is followed by Westphal. But the 
reading of M is quite unexceptionable. Marquard’s objection to 
the two participles SypAfiepa and laa opra, which are not co¬ 
ordinated in sense, is groundless. In the active one might 
have ov Svpofieda ravra riOepai icra opra €^^9, which would 
become in the passive ov dvparai ravra rideadai ura opra i^rjsy 
and if used participially ov Svmfiepa ri6€(r6aL itra opra 
Another objection to the readings of Meibom and Marquard 
is that they would require ndepaiy not rideadai. 

P. 167 , 1 . 6. Before otto Se rov diropovy the MSS have otto 

ropiov fX€P eVl to o^v 8vo 6801 Kai eVl to j3api» 8vo, This sentence 

cannot be retained; for in the first place it makes a false 

u 2 



assertion, there being but one progression upwards from the 
semitone or first interval of the Diatonic tetrachord (that is, 
of course, in the scale of any one shade^ see p. 159, 1. 12); 
and in the second place, referring as it must, along with the 
preceding paragraph, to the Diatonic genus only, it could 
not stand in such close connexion with the following propo¬ 
sition, which as it concerns the ditone can only apply to the 
Enharmonic Genus. 

1 . lo. €7rl Se TO jSapii ttvkvov fiovov which in some of the MSS 
follows TO o^v is a most silly interpolation. The sentence 
in 1. II, XeineTui fxiv yap k.t.X., introduces the proof of the 
assertion nXeiovs Se rovrayv ovk etTovrai in 1 . 9. The consideration 
of the descent from the ditone does not begin till 1. 13, eVi Se to 
jSapo pia* dedeiKrai yap k.t.X. 

P. 168 , 1 . 15. I read Kara with R. The other MSS have 
KaL But whichever we read, to too ttvkvov pey^dos is accusative 
(whether governed by Kad" or Kara) and not nominative, as 
Marquard and Westphal suppose. Evidently the chromatic 
interval that corresponds to the enharmonic ditone (which will 
differ in size as we pass from one shade to another) will vary 
inversely as the size of the Pycnum. to ye pearjs of the MSS, 
earlier in the sentence, is quite correct. 

P. 159 , 1 .15. I have corrected ei to 17. Cp. p. loi, 1 .13, where 
Westphal has corrected eiTrep to f^Trcp. The MSS of Aristoxenus 
exhibit perpetual confusion of i, e, 17, u, ei, 01. Cp. note on p. 
loi, 1. 7. 

1. 18. 8 vvap€L9 . .. €L8rj .. . deaeis are used in a general not 
a technical sense here. 

P. 161 , 1 . 24. The absurd irri which appears in the MSS is 
really the iirci of p. 162, 1 .1. This is proved by the Selden MS, the 
writer of which after the pia 686s cKarepa ea-rai of 11. 23-24 
missed a line, and proceeded to write the 8€ikt€ov eVl (for eVei) 
of p. 162, 1 . I. Then discovering his mistake he drew his pen 
through these latter words. 

P. 162 , 1 . 4. Whether we retain kot ov8iT€pov t&v Tp67roi>v of 
the MSS or read as I prefer kqt oiScrepov r^v totto^v the sense 
is ‘ neither above nor below.’ 

1. 8. The MSS read oTroreptos av T€0rj TO 8ltovov' tottw tovov 


T€ 0 €Lfi€Pov. Marquard followed by Westphal reads oTrorepco? av 
Tedrj TO birovov* eVi Se avr^ tottio tovov redeifievov #c.t.X., taking 
o7roT6pQ)9 in the sense of ‘ whether above or below ’ on the analogy 
of /car’ oibirepov Tcav TpoTTcav (1. 4) > S-^d eVi t© out© tott© in the 
sense of irpos tw €lprjpL€v<a <f>d 6 yy<a. But this last is very hard 
to accept; the phrase would much more naturally mean ‘in 
the same direction of pitch’ i.e. either ascent or descent. 
I prefer, having read kqt ovbirepov tcdv Tonoiv in 1. 4 = ^1^ 
neither of the directions,’ to read here onoTepcDs &p reOrj to 
hiTovov tS)v T07rQ)i;=‘in whichever manner the ditone be placed 
in regard of the directions.’ The two tottoi are 6 eVl to o|u and 

6 €7ri TO ^apv. 

1. 21. The MSS reading is obviously defective. The words 
I have introduced restore the sense simply. Marquard’s in¬ 
sertion of the article before (l)d6yyovs is quite inadequate. 
Westphal reads eVl ttjv avT^v tociv tovs €ipT)p,€vovs iv ttukvc^ 

P. 163^ 1. 4. oTi Sc TO biaTovov avyKeiTai rjToi k.t.X. The pro¬ 
position of this paragraph seems at first sight inconsistent 
with Aristoxenus’ exposition of the shades (see p. 142, 11. 9-14); 
according to which exposition there are only two shades of the 
Diatonic genus, (a) the soft Diatonic, the tetrachord of which 
is thus divided 






















(in which i = ^ of a tone) 
(d) the sharp Diatonic with the tetrachord 


















1 i i i 

If we complete the Fifth by adding to each of these tetra- 
chords the disjunctive tone = 12, we shall have in the sharp 
Diatonic 12 and 6 as the only dimensions of intervals. In 
the flat Diatonic, on the other hand, we shall have four 



dimensions, 6, 9, 12, 15. But how can there be a Diatonic with 
three dimensions? In this way, that it is allowable for the 
Diatonic scale to borrow the Chromatic Parhypatae. Thus, by 
a combination of the Sharp Diatonic Lichanus and the soft 
Chromatic Parhypate we obtain a Fifth of the form 






















which may be called Diatonic from its prevailing character. 
In it there are three dimensions, 4, 12, 14. 

P. 164 , 1 . 13. etSof here = schema = the ‘ figure’ or order of 
disposal of the given parts of a whole. 



dya$6s 122 . 8 , lo, 13 . 

^Ayfjvojp 127 . 25 . 

dyuoicj 125. 3 ; 126. 26 ; 127. 2 ; 

136. 19 ; 144. 21 . 
ayvoia 131. 12 , 14 ; 151. 7* 
dycj 104. 5 , 6 , 9 , 24 ; 128. ii; 
144. 16 ; 159. 22 . 

of movement’ 105. 
14 ; 125. 17 . 

= ‘ sequence ’ 121. 7 ; 143 .18 . 
= ‘ keeping,’ ‘ observance ’ 

128. 10 . 

ddid<popos 129. II. 
ddvvaT€OtJ 106. 25 . 
qdo) 102 . 25 . 
drjp 134. 27 . 

dBeijprjTos 126. 25 ; 127. i* 

^ASrjvaTos 128. li. 

aiaSdvofjuu 98. 20 ; 125. i^ 2 , ; 

129. 22 . 

atcrdrjffis 99. 21 ; 101. 22 , 24 ; 102. 
8 ; 103. 5 ; 104. 5 ; 111. 13 ; 
124. 4 , 23 , 27 ; 129. 22 ; 139. 
3 , 10 , 19 ; 140. 9 ; 145. 18 . 
aiaOrjTos 99. 6 . 

ahla 98. 24 ; 114. 18 ; 123. i; 
124. 9 ; 126. 18 ; 133. i; 

134. 2 , 3 ; 138. 12 ; 145. 17 ; 
151. 10 ; 153. 9 ; 159. 26 ; 160. 
21 ; 161. 17 , 20 ; 164. 7 , 10 . 
amos 114. 9 ; 115. 6 ; 118. 22 ; 
122 . 16 . 

d/capicuos 145. 16 . 

dKLvrjros 113. 23 ; 151. 17 ; 152. 

6, 9 , II. 

dKoi} 102 .15 ; 106. 24 ; 107 ; 124. 
16 , 17 ; 129. 17 . 

dKoXovOicj 126. 19 ; 138. 16 ^ 17 ; 

143. 23 ; 154. 14 , 16 . 
dKovcj 108. 8 ; 122. 8 ^ 19 ; 123. 6 ^ 
12 ; 149. 12 . 

dupl^eia 125. i. 

d/cpifiris 97 . 8; 103. 6; 108. 9 ; 
124. 5 ; 144. I ; 145. 19 ; 146. 
23 . 

dKpifioXoyeofJiai 126. 15 . 
dicpi&w% 119. 3 ; 124. 19 . 
dxpodofmi 123. 2 . 
dKp6aais 122 . 8 . 

dfcpos 121 . 8 ; 137* 2 ; 141. 2 ; 

147. 8 , 20 ; 148. 7 . 
dWoiojffis 130. 24 ; 164. 17 . 
dWorpioXoyicj 124. 4 . 
dWdrpios 124. 8 . 

0 X 0705 108. 23 ; 109. 12 . 
dpL&pTrjiia 132. 13 . 
dfiapria 123. 5 . 

dfi€\(v^Tos 113.1 2 ; 117 .8 ; 120. i. 
dfJupKTSrjriaj 138. 22. 

dpupiaPiqTTjffis 118. 7 * 

dvdyo) 124. 15 ; 132. 14 ; 133. 5 , 


dvaycjyrf 133. l; 134. 2 . 
dvcupioj 110. 24 ^ 25 ; 145. 3 ^ 
dvajidprrjTos 133. 6 . 
dvairddciKTos 99. 2 , 17 , 19 ; 129. 9 . 
dvdpfjiocrros. 110. ii, 17 J 143. 6 . 
dva<popd 106. 23 . 
dpemKfjirros 108. 14 . 
ayeffis (see note on 103. 16 ) 97. 
10 ; 103; 104; 105. 19 ; 106. 
II; 114. 9 . 
dvrjp 112 . 18 . 
dvOpomiKos 106. 17 . 
dviTjfxi 103. 12 ; 104. 3 , 5 ; 110. 7 ; 
115 .17 ; 123. 24 ; 132. 19 ; 133. 
I; 137. 15 - 

dpofLoios 125. 18 ; 139.. 7; 150. 16 , 
17 ; 162. 16 , 23 . 
avTiarpitpcj 138. 4 . 
dvurr^pov 95. ii. 
dvorripo) 101. I 2 . 



di/wraros 111. II. 
d^ioXoyos 98. 14. 

d^iSo) 95. 9; 138. 7; 140. 9; 143. 

dopiffTos 99. I. 
diraiT€0J 134. 25. 
diraWaTTO) 104. lo; 124. 22. 
aira( 141. 12, 13. 
diTCipla 160. 3. 

dncipos 97 . 15; 104. 4; 106 ; 107; 
112. 2; 138. 20, 21; 144. 3, 5 ; 
158. 22, 24; 159. 5, 7, 15. 
dirixo^ 137. 7; 155. 6, 8. 
dir\ovs 109. 20, 22; 110. 25; 125. 

24; 129. 3; 131. 9. 
dTTAws = (i) ‘in plain speech, not 
in accordance with strict philo¬ 
sophical truth’ 102. 14. 

= (2) ‘roughly speaking, 
overlooking particular excep¬ 
tions’ 125.6; 126. 2, 25 ; 127.5. 

= ( 3 ) ‘ in general terms, sum¬ 
ming up particulars’ 131. 8; 
143. 15. 

= (4) ‘absolutely, without 
exception’ 127. 20; 150. 15; 
153. 4; 156. 5. 

= (5) ‘in the abstract’ 136. 

dnoPdWoj 139. 6. 
ditoPKlitcj 104. I. 
diroyiyvwfffcoj 122. 18. 
dirodci/cvvfjLi 99.9^ ii ; 118. 4; 124. 
13 ; 153. 9. 

diTohuKTiKos 99. 2 ; 129. 9. 
dnodeifis 124. 2, lo; 134. 25. 
dirobiboofu 98. 9, lo; 99. 13; 103. 
15; 108. 8; 113. 3; 119. 16; 
128. 9; 131. 17 ; 143. 17 ; 144. 
I, 2. 

dirohoffis 128. II. 

dwoOcffTrl^aj 124. 9. 

diroXifjLTrdvoj 135. 2. 

ditop^w 149. 12 ; 164. 5. 

dnoripLVCJ 96. 6. 

dnoKpatvoj 105.6 ; 119. 17* 

awTo; 95. 17; 96. 10; 98. 16; 99. 

24; 114. 6, 21. 
diTvKvos 120. 13. 
dpifffco) 122. 19. 

'Api(TToT€\rjs 122. 7> 20. 


dp/jLovla (see note on 95. 5 ) 95. 
10 ; 115. 9 ; 116. 9 ; 118. 15 ; 
126. 9 , II ; 127 . 23 ; 135. 5 ; 

139. I, 3 , 9 , 12 ; 142. 19 ; 154. 
22 ; 155 . 15 ; 160. 5 , 16 ; 163. 
19 ; 164. 8 . 

dppLoviKos 123 .19 ; 130. 7 ; 134. 24 . 
apfLoviKSs, 6 95. 18 ; 96. 12 ; 98. 
19 ; 101. I ; 119. 15 ; 128. 10 , 
13 ; 131. 13 . 

dpfioviK'fi, 17 95. 5 ; 101. 11; 126. 

3 ; 130. I; 134. 10 . 
dp/AoviKd, rd 123. 7 . 
dpfxoTTO) 104. 2 ; 107 . 23 ; 110. 8 ; 

133. 17 , 18 , 19 ; 139. 1 ; 147. 13 . 
dpxaiKos 115. 2 . 

dpxh 98. 13 ; 108. 14 ; 119. 4 ; 
123. 4 ; 124. II, 27 ;* 131. 5 ; 

134. 19 , 20 ; 145. 2 ; 146.21; 
147. 21 . 

dpxo€tdris 134. 22 , 25 . 

dpxo/Mi 101. 13 ; 109. 16 ; 126. 

11 ; 134. 26 ; 135. i; 142. 7 . 
darpafiiis 133. 6 . 
darpoXoyia 122. 13 . 
dfTVfJtpLcrpos 115. 23 . 
daviKpojvos 120. 21 ; 144. 20 . 
dovvO^Tos (see note on 108. 22 ) 
drafta 99. 4 . 
droTTia 131. 19 . 

droiros 131. 14 , 21 ; 132. 12 , 13 ; 

140. 17 . 

avXioj 112. 16 ; 130. 5 ; 134. 2 , 3 . 
avkonoita 134. 8 . 

avkds (see note on 112. 13) 112. 
13; 128.17,18; 130.4; 132. 
12 , 16 ; 133.3,5,7; 134.1,4,7. 
av(dpoj 106. 20 ; 112. 2 ; 137. 14. 
av^rjais 97. l6; 107. 17 5 119. ii; 
138. 18. 

avrdpKrjs 100. 13; 123. 16; 127. 

3 ; 144. 21 ; 145. 10 . 
d<paip 4 oj 132. 25 ; 146. 7> ^9 > 

147. I. 

dipav’^s 103. 10. 
dflrjpu 100. 7 f 108. 25. 
dfpiKviofxai 105. 24; 115. 9, 16; 
137. 15- 

d<pl(XTTjpLi 114. 13 ; 115. 14 ; 128. 
22 ; 133. 22 . 


dipopi^a) 98. 3; 108. 5 ; 109. 24 ; 
111. 2, 20, 22 ; 113. 8,15 ; 118. 
13, 18; 143. 14; 144. 13; 146. 
24; 151. II ; 164. 17. 
d(popi(TfA6s 111. 3. 
dxprj(TTos 129. l ; 145. I3. 
dipvxos 132. 5. 

0adi(aj 122 . 4 . 

0apvs (‘ low ’ in pitch) passim, 
fiapvTTjs 97 . II ; 103; 104; 105; 

pcpaiooj 133. 7 ; 134. 4. 

122. 3; 123. 3, 7* 
ffpaxvs 101 . 4 . 

y€V€(ns 129. 19. 

yipos (see Intr. A, § 6) passim, 

yeojfjtirprjs 124. 22. 

y€OJfA€Tpia 122. 13. 

yXvKaivcj 115. 6. 

yvcjpi^cj 127. 7. 

yvdjpifws 105.4; 106.13 ; 107. 20; 

113. 7; 131. 12 ; 135. 10, 16. 
ypdfifja 119. 6, 8 ; 128. 2, 3. 
ypapipy 124. 21. 
ypdcpcj 130. 9, II, 13 ; 131. i. 

d€T£is 123. 8. 
de/cTiKos 108. 2. 

hiopai 114.19; 133. 20 ; 138. 20 ; 
160. 9. 

dexopai 118. 6. 

drjkocj 96. 2. 

diafiaivo) 102 . l, 16 . 

didyvojffis 100. 14; 127.4; 7* 

didypaptfJLa 95. 21 ; 96. 2; 101. 6 ; 

119. 16 ; 124. 20. 
dia(€vypvfu 109. 17; 149. i, 15; 
150. 14. 

^id^ev^is (‘disjunction’; see Intr. 

A, § 12 ) passim, 
biaipeais and hiaipioj passim, 
hiaiaOdvopai 107. 5 ; 126. 10, 13 ; 

130. 18 ; 131. 4. 
hidK€vos 118. 5. 
diafcpifiSoj 108. 14. 
di€i\€yopcu 96. 21; 102. 20, 25; 

110. 7 ; 119. 7 ; 128. 3. 
diapapTavo) 99. 21 ; 110. 18 ; 130. 
7 ; 132. 9, 23; 136. 19. 

diaptipo) 122. 19; 133. 14; 139. 

22 ; 140. I, 6. 
diavoeoj 132. 5. 

hidvoia 124. 16, 18; 126. i ; 129. 

Btairopia 140. 21. 
dtaaa<p€CJ 107. 4. 

diaaKoirioj 111. 16. 
hiacTaais 97. 15 ; 106. 14, 21 ; 
107. I, 9,12, 15; 112. 12 ; 128. 

diaartjpa (‘ interval ) passim, 
diaarrjfiaTtKos passim, 
hiaaw^cj 133. 15 . 
diareivaj 112. 11 ; 125. 6 . 
diaTeXioj 102 . 19 . 
diarovos (see Intr. A, § 6) passun, 
diarpifio) 115. 8 ; 126. 10 . 
dta<pv\dTTCJ 119. 13 . 
diaxpojvioj 136. 12 . 
hia<pwvia 111. 16. 
dtd<pcjvos (see note on 108. 21 ) 

di4(€ipi 96. 14; 101. 21; 103. 13. 
di€(ipxofJiai 103. 12 ; 106. 18; 134. 

^ 3 - 

diipxopm 97 . 19 ; 101 . 16 ; 106 . 

13 ; 126. 3 ; 142. 2. 
dUais (any interval smaller than 
a semitone) passim, 
hiix^ 119. 18. 

dirjyiopm 122 . 7* 
hiopdoj 127. 10. 
hiopify) passim, 

diirkdaios 117• 7 5 120. 8 ; 137. 14. 
diirkovs 109. 20, 22. 
dirovps passim, 

6/X" 98. 22. 

3o^a 96. 12 ; 104. 24. 
do(dCctf 103. 25. 

dvvapis 95. 6 ; 96. 14; 113. 4; 
124. 18, 23; 125. II; 127. 5, 
9 ; 130. 24; 131. 2, 7 ; 138. 
10; 140. I; 159. 18, 20. 
dcjdeKaTTjfiSptop 117. 
dwpios 128. 

€ 00 ) 159. 15. 
kyyiypofjuxi 98. 8. 
kyyvs 115. 9, 13 ; 120. 7. 
kSi^o) 124. 20, 23. 



eTSos 97. I; 139; 150. 9, 16^ 19; 

159; 164. 
itcaripcjOev 121 . 8. 

€fcfc€ifxai 95. 12 ; 135. 6 , t 6. 

IkkKivoj 124. 4. 

€K\a/jLPdvaj 108. 7. 

^KkifAirdvo) 124. 4; 150. 24, 25. 
€fcfi€\‘qs (‘violating the laws of 
melody ’) passim, 
itcTTjfiopiov 117 • 7* 
kXdrrojais 97. 16 ; 138. 18. 

108. 12. 

kfifiek^qs (‘ musically legitimate 

€fiir€t/)os 123.13 ; 124.12 ; 126. 14. 
kfimirroj 134. 27 ; 150. 24 ; 160. 3. 
kpupatvofjuii 139. 15, 17. 
li^dAA.a£ 102. 18 ; 154. I ; 156. 9. 
kvapyrjs 103. 14. 

IvappLovios (see Intr. A, § 6) 

€V€lfU 96. 23. 

€V€py4cj 133. I. 

iviarrjpu 102. lo. 

€Woia 95. 20; 98. 12. 

€VT€ivcj 133. 13. 

Ivros 135. I. 
kptmdpxctJ 130. 20. 
h^ahvvarioj 107. 3 ; 119. 23. 
€(aip€Tos 141. 4. 

€(api6fA€aj 99.19, 24; 100. 8 ; 124. 

10; 127. 19, 2 ly 24. 
h^^rd^cj 99. 22; 115. 21; 146. 22. 
e^is 98. 7; 123. 19. 

4(opiC<» 115. 5. 
kwdycj 114. 16; 115. I. 
kiraycTfq 97. 23; 144. 4. 
kitakXdrrcj 115. 14; 150. I, 12. 
hiravdyoj 147. 9. 

€ira<pdofjuii 98. 2. 
kireOi^o) 124. 19. 
kmfikinw 126. 12; 159. 3. 
*Emy6v€ioi 97. 6. 
kmfJi€kris 96. 2. 
kmnkeiov 105. 17* 
emirokrjs 164. 7. 

€m(rK€tj/is 111. 18; 127. I7> 23. 
kmaKoirkcj 96. II ; 98. 25; 103. 
22; 107. 19; 114. 7; 130. 18; 
160. 2. 

Imararkoi 132. 3; 133. 10. 


kmarrjfjLfj 95; 101. ii; 130. 8,15 ; 

131. 16, 20; 134. 18; 159. 15. 
lirlraais (see note on 103. 16) 97. 

10 ; 103 ; 104 ; 106. ii ; 114. 9. 
kniTclvo) 103. 13 ; 104. 3, 4; 110. 

6 ; 115.16; 123.23; 132.19; 

133. I; 137. 16. 

^EparoKkijs 98. 21 ; 99. 18. 

€pyov 131. 18 ; 132. i, 2. 
kpiariKos 122. 17. 
kpfxrjvela 108. 14. 

€vdaifAovia 122. II. 

€vbrjko5 114. 21. 
evOicjs 125. 6 ; 159. 19. 

€v6vs 121. 9 ; 124. 21, 23. 
€VKaTa<pp6vrjTos 123. 14. 
evavvoiTTos 96. 12. 

ZatcvuOios 127. 25. 

^6os 115. 10; 123. 7, 10; 131.13. 
ijkiKia 112. 20. 

^/jL€pa 128. 10 ; 133. 13. 

^fxiokios 116. 14 ; 117 ; 141; 143. 
4, 5 ; 155. 7. 

Tjfutrvs 113. 10; 115. 14; 116. i; 
136. 14, 15 ; 146. 22 ; 147. 10, 

^/jLiToviaios 142 ; 143. 4, 12. 
^furSviov passim* 
iip^piio} 104. 13; 105. I, 12, 23; 
113. 21. 

^p€fjua 105. 13, 16, 20, 25. 
i^pfio(Tpi€vos (see note on 95. 3) 97. 
23 ; 110. 8, 22, 23, 25 ; 111. 8 ; 
125. 25 ; 129. 14; 132 ; 133 ; 

134. 5 ; 145. 3; 151. 18. 

Oavpud^oj 151. 3; 158. 22. 
OavpuoLards 99. 3 ; 122. ll; 133. 9, 

eiais 99. 17; 145. 5 ; 156. i, 24; 
159. 18. 

Oecjpeoj 95. 11, 14 ; 98. 4; 101. 18 ; 
111. 4; 112. 21; 124. 18; 127. 

12) 15* 

Ofojprjrifcds 95. 7* 

$€ajpla 95. 8; 101. 10; 123. 22 ; 
124. 14 ; 130. 4. 

iafxPi/c6s 130. II, 12. 


ihla 95. 2 ; 101. 20. 
i^ios 107. 13; 114. 4; 118. 14; 
130. 20; 134. 8 ; 136. 6 ; 138. 

13, 19; 139. 18; 142. 19; 
151. 17, 23; 152. 18. 
idiorrjs 110. 14. 
idiwTTjs 131. 17, 21. 
iKavws 96. 15 ; 105. 17 ; 108. ii ; 
115. 2. 

iffTrjfxi 101. 23; 102 ; 103 ; 104 ; 

105; 106; 107.24; 118. 4. 
iaxvpos 131. 14. 
icrxvs 122. II. 

KaOapws 127. 10. 

KaOrjKOJ 101. 14. 

Kadiarrjpu 103. il. 
fcaSoKov 97.17, 19 ; 98. 5 ; 99. 23; 
100. 20; 101. 6, 8; 104. 24; 
110. 21 ; 111. 5 ; 116. 10; 125. 
22 ; 125. 21 ; 132. 13; 133. 8 ; 
134. 25 ; 140. 3 ; 149. 13, 17. 
Kadopdo ) 96. 16. 
mipos 101. 14. 

K&iiirTCJ 135. I. 

KarayiyvwtfKOJ 99. 5 ; 131. 19. 
Korahvcj 132. 6. 

KarafAavddvcj 96. 6 ; 100. I, 12 ; 
103. 25 ; 106.1; 108. ii ; 113. 
16; 126. 16. 

tcarapLCfMpofJULi 122.15. 

Karavoioj 104. I, 21 ; 105. 22 ; 
108. 10; 112. 19; 114. 15; 
120.4; 136.22 ; 137.14; 138. 
17 ; 142. 26 ; 147. 23. 

KarawKvoa) 101. 6. 

KaraiWKvojais 101. i ; 119. l6 ; 

128. 25 ; 143. 16. 
fcaTa ( TK € vd(aj 124. 5; 131. 20. 
Karaando ) 112. 15.^ 

/ carixc ^ 113. 18 ; 114. 4; 115. 3 ; 

120. 23; 139. 15 ; 141. 3. 

Kivio) and Kivrjms passim, 

KoiXia 132. 17. 

Koivorris 151. 3. 

Koivcjvkcj 118. 15 ; 150. 6; 163. i. 
KopivOios 128. II. 

Kpivcj 106. 24, 25 ; 107. 13 ; 124. 
17, 19; 126. I ; 131. 22 ; 132. 

KpiTTlS 131. 20. 

Kvpios 132. 10 , II; 133. 20 . 

XavOdvcj 103. 13 ; 122 . 6 . 
hdaos 97 . 6. 

Xeiiro) 116. 3 ; 120. 15 , 24 ; 141. 
19 ; 152. 2 , 12 ; 157. ii, 15 , 
21 ; 158. 3 , 10 ; 162. 23 . 

Xi^is 110. 16 ; 119. 6 . 

Xrfif/is 143. 3 ; 145. 20 ; 146. 6 . 
Xixayoeid'^s 118. 6 . 

Xixai'Ss (see Intr. A, § ii) passim, 
XoyiKos 102. 20 ; 103. 7 . 

Xdyos 98. 27; 99. 3; 107. 18; 
ioS. 9, 12, 14; 122. 12; 123. 
8, 16; 124. 6, 8 ; 125.16 ; 127. 
20; 129.8; 133. 20; 138. 7; 
144.1 ; 149.16 ; 151.6; 160. 9. 
Xoydt^s 110. 4, 5. 

Xvdios 128. 

fidBrjim 122. 12 ; 123. 6 , 15 . 
luiXaK6s 141; 142; 143 ; 155. 7- 
IMvOdvoj 131. 21 . 

fjLcXonoiia 314. 19 ; 315. 4 ; 123. 
9 ; 126 . 14 ; 129 . 10 , 14 ; 131. 
10 . 

fiiXos 95. 3 ; 96. 19 ; 97 . 20 , 22 ; 
98. 3 , 23 ; 99. 4 ; 100. 17 ; 
101. 9 ; 103. 5 ; 107 . 16 , 23 ; 
110; 111; 112. 3 ; 113. 2 ; 120. 
6 , 17 ; 121. 4 ; 123. 23 ; 124. 
14 ; 129. 12 , 19 ; 130. 2 , 14 ; 
134. 4 ; 135. 6 ; 143. 15 , 18 ; 
144. 16 ; 159. 17 . 
fi€X(vd€a) passim, 

pieX^Sia 96. 3 , 7 ; 101 . 2 ; 119. 5 ; 
120. 4 ; 129.6; 144. 7 . 

fLcXqtdiKos 103. 8 . 

fiipcj 106. 2 ; 116. 5 ; 125; 126. 2 , 
6 ; 137. 3 ; 139. 21 ; 140. i, 4 ; 
142. 2 . 

pL€pi^a} 98. 5 ; 109. 15 , 19 . 
fieai] (see Intr. A, § ii) passim, 
fL€TafidXXa) 134. 2 . 
pL^rafioXii 101. 8 ; 125 .14 ; 129. 4 , 
5 , 7 ; 131. 9 . 

/jLcrdPoXos 129. 3 . 
fl€TaKlV€0J 104. 6 . 
fjLcraXafjiPdyaj 133. 9 ; 158. 14 . 
fLerax^ipiC^fuii 99. 5 ; 100. 19 . 
fierixof 160. 5-17 ; 163. 3 . 



li^roxh 162. 17 . 
fA€Tpicj 115. 22; 141. II, 12. 
/jLerpitcri 128. 20; 180. 9. 
ptirpov 112. 21 ; 180. 9, il; 141. 


fxrjOeis 95. 9. 
piyvvpu 100. 9. 
fiiKTos 109. 17; 185. 7* 
fu(is 100. 12. 

Mi(o\vdios 128. 14, 23. 

MiTvKrjvdios 127. 25. 
pLvrjpLTj 129. 22. 
fi,ur]fAov€voj 129. 23. 
fjLokis 111. 12. 
fiovri 104. 22. 
piop<P‘q 129. 12. 

/jLovffiKos 98. 3 ; 110 . 4 > 1 7 > m* 

I ; 124. 15. 

fwviTiKos, 6 95. 15 ; 128.6, 18,19; 
124. 27. 

pLovaiK-Qj if 95. 15; 98. 3 ; 99. 4; 
144. 6, 21; 128. 9, n ; 124. 
12; 125. 4, 25; 129. 20, 21, 
24; 188. 12; 159. 14. 

V’qTTj (see Intr. A, § ii) 125. 10; 

188. 9; 144. II. 
vryrwv (see Intr. A, § 29) 131. l. 

voicj 97. 13; 107. 16; 108. 6; 

113. 17 , 20; 118. 3; 123. 22. 
vorjrds 124. 5. 

(vWafiri 119. 8; 128. 4. 

(vv€<Tis 97. 10; 125. 4; 131. 4; 
182. 2, 6. 

^vviriiAi 107. 5; 108. 12; 129. 17; 
130. 3; 131. 22. 

bUs 122. 4; 157 ; 158 ; 159 ; 160; 
161; 162. 
oifccTos 185. I. 
oiKeiorrjs 100. 23. 
bicrairkaaios 119. 23. 
dKTCLxopbos 96. 3 ; 127. 22. 
okiycjpicj 143. 18. 
oAws 96. 14; 97. 13; 123. 12; 

127. 21 ; 145. 15. 
dfmkSrrjs 105. 2. 

bfioios 139. 7 ; 145. 3 ; 149. 3, 4; 
150. 7-19. 


ofjioicjs 189. 21 ; 152. 9 ; 158. 13 , 
16 . 

ofjtokoyeoj 114. 15 ; 124. 3 ; 134. 

ovopui 105. 8 ; 110. 6 ; 114. 4 ; 

122. 17 ; 138; 140; 164. 14 . 
ovofm^cjlOl, 25 ; 102. 22 ; 104. 20 . 
of vs (‘ high’ in pitch) passim, 
b^vTTis 97 . II ; 103; 104; 105. 

22 , 24 ; 106. 
opyaviKos 106. 17 . 
opyavifcrj, 17 123. 20 . 
bpyavov 104. 4 ; 112. 9 , 12 ; 124. 
15 ; 126 . 10 ; 132; 133; 134. 

5 .6. 

bpOos 133. 6 . 

opdws 110. 13 ; 132. 5 ; 134. 16 ; 

146. 21 . 
opfjidoj 105. 6 . 

bpos 140. 3 ; 146. 12 , 24 ; 149. 17 ; 

otraxSfs 97 . 18 . 
ovSds 133. 7 . 
o<p€kos 133. 4 ; 145. 2 . 
6 <pdak/jL 0 €idffs 131. 17 . 
6<p0akiio<pavrjs 132. 2 . 
b^is 124. 23 . 

iT&Oos 102. 26 ; 104. 7 > 6 ; 

136. 6 ; 159. 8 . 
irais 112 . 18 . 

irakaios IIZ. I 9 ; 144. II. 
iravT€kws passim, 
iravTobairos 125. 22 ; 129. 12 . 
irapaPakkoj 132. 25 . 
irap&bo^os 103. 21 ; 122. 14 . 
irapatcokovOioj 129. 18 , 24 . 
irapaKovoj 123. ii» 
irapakapL^&vcj 98. 14 ; 136. 2 . 
irapakifAirdi/cj 126. 24 . 
irapafxiar] (see Intr. A, § 11 ) 125. 

9 ; 137. 20 ; 138. 12 ; 158. 20 . 
napavrirrj (see Intr. A, § 11 ) 138. 

9 , 10 ; 144. 12 . 
irapairkriaiojs 119. II. 
irapaarjpuilvcj 130. 2 , 17 ; 131. 15 . 
irapaarjiiavTiidi 130. 8 , 15 . 
iTaparrjpio) 108. 8 ; 134. 26 ; 139.6. 
irapOkvios 112 . 13 . 
iraptnraTrj (see Intr. A, § il) passim. 


irapviroXafiPavo) 122 . 6 . 
vavofiai 142. 6 . 

hid ir€VT€y TO (‘ the Fifth ’) passim, 
•n^palvoi 106. 15 ; 159. 14 , 19 ; 

161. 3 , 16 . 

ir 6 /)as 101 . 23 ; 107. 9 ; 112 . 12 ; 
115. 15 , 17 ; 122. 13 ; 130. 3 , 
7 ; 131. 16 , 22 ; 132. 2 , 10 . 
irepiyptupri 98. 5 . 
ir€pi\apLPdvoj 138. 6 . 
ir€pi<p€pr]s 124. 24 . 
ircpiipopd 100. I. 
mOavos 144. 4 , 8 . 

mwroj 146. 17 ; 156. 13 , 16 , 23 ; 

162. 6 , 10 , 21 . 
mar€vo) 145. 18 . 
iT\ai/do/mi 134. 7 . 
irKdvrj 151. 2 ; 158. 21 . 

irXdTos 97 . 7 . 

nAaro;!^ 122 . 8 . 
iT\€ovaxi»is 164. 21 . 
irKfjOos 143. 19 . 

7r\ovTos 122. II. 
itV€vpLa 132. 4 . 25 . 
iroirjTiKTf 95. 12 . 
iroAAairA.a(nos 120. 8 . 
iroWairKovs 109. 21 , 22 . 
iroXvfieprjs 95. 3 . 
iTop€vopLcu 122. 5 ; 129. 15 . 
iTopporripoj 96. 9 ; 131. 3 . 

TTovs 125. 15 - 23 . 

irpayimreia and irpaypuiTevopiai 

irpeafivTaros 111. 9 . 
irpoairoheiKPVfu 100 . 2 . 

irp60ki]im 134. 18 , 22 ; 151. 2 ; 

153. 3 ; 158. 21 ; 159. 3 . 
irpoyiyvwaKCJ 122 . 4 . 
irpohicupicj 109. 24 . 
irpohiavoicj 134. 12 . 
npohiipxofiai 122. 3 ; 134. 10 . 
irp6€i/u 110. 25 ; 123. 16 . 
irpoeKriSrjpu 122 . 18 . 
irpoOvfA€o/juii 120 . 5 ; 128. 25 . 

irpoKaraaKcvd^o) 147. 7 . 
irpoadycj 115. 9 ; 133. 17 , 18 . 
irpoahiofjiai 110. 9 ; 145. li. 
iTp6(r€ipLi 122 . 9 , 17 . 

irpoaipxopiai 115. 13 . 
irpoaix^ 120. 2 ; 134. 21 . 
irpoarjyopia 113. 19 . 

irpoarifcoj 95. 9; 104. 9; 132. 21; 
134. 19. 

irp6aK€ipm 147. 24; 148. 5. 

irpoardrTU 145. 20 ; 141. 5. 

irpoaTvyxdvcj 111 . 10 . 

irpoaahia 110 . 5 . 

irpoundpxcn 134. 14. 

irpox^^pos 132. 6. 

nrajais 107. 21. 

nv^a7o/)as 127. 24. 

irvKvov (see note on 116. i) passim, 

firfTos 108. 23; 109. 13. 
poirri 110. 13. 
pvOfjLiKTj 123. 20. 
pvOpLoiToita 125. 22. 
pySfios 125. 15, 23. 

aa<piis 105. 17. 
aaipais 97* 9* 

arjfjuiivaj 100. 22; 125. 23. 

(rT]fji€rop 95. 20; 115. 7; 130. 19, 
20; 131. I, 2; 135. 19. 
aiojirri 101. 24. 

<rK€\f/is 102. 10. 
ardais (^stopping*) 104. 22. 
aroix^Tov 120. 12; 134. 12. 
CToix^iwhris 95. 6. 

(rroxd^optai 115. 7. 
adyKUpai 110. 5 ; 117. 17. 
(TvyK€xvfJL€PCJs 97. 14; 103. 25. 
cvyxopthia 114. 2. 

(Tvyxottpicj 114. 16, 17; 148. 3. 
av^vyia 125. 19. 
avpimvTCJ 104. 25. 
avpLirkrjpoo) 152. 20. 
av/iirpodvpiio/juxi 108. lo. 

(Tvpupcjvecjy (TVfKpcjviay and ovfi- 
(pojvos (see note on 108. 21) 

awdycj 106. 21. 

avvapL<p6T€pos 109. 15; 159. 26. 
(TvvditTCj 109.16 ; 149. 1,15; 150. 


(Tvv€ulyff (‘conjunction^; see Intr. 
A, § 10) passim. 

(TvveOi^oj 111. 13; 115. i; 125. 

25 ; 126. 14. 

(Tweipot) 143. 21. 
ayv€maiTd(i) 115. 10. 
avvix^io. 98. 7 5 3> 



ow€xvs 101. 20, 21; 102. 15, 20; 
103. 2, 7, 18 ; 109. 20; 119. 5, 
15; 120.3,10; 143.17; 144. 
12; 145.9; 1^7- ^7* 

(Tvi^cx^^ 101 . 24; 102 . 3 , 19. 
(TvvScffiSy avvO^roSy and awriOruxi 

(Tvvlarrjfu 99. ii; 110. 8 , ii; 144, 
24; 151. 19; 163; 164. 
avvop&cj 106. 16; 113. 6 ; 114. 16; 
131. 6, 15; 134. 17, 24; 141. 
19; 147. 22; 151. 8; 160. 19; 
164. 23. 

avvT€lvoj 95. 8; 101. 9; 144. 14. 
(Ttn/TofKus 107. 21. 

(TvvTovos 115.5 ; 116. ii, 24; 117; 
118 ; 137. 6 ; 139. 3 ; 142. 9, 
12; 143. 9, 10; 163. 10. 
avvvirdpxoj 106. 7. 

(Tvpiyi 112. 16. 
avpiTTCj 112 . 16. 

avaraais 99. 4; 107. 16; 110. 13. 
(TvffTrjfAa (‘ scale ’) passim, 
aX ^ P - o . 96. 4; 99. 15,16, 25 ; 100. 
2; 125.12,21; 130.22; 149. 
3> 5 > 164. 13. 

98. 22. 

rafts 95. 5; 96. 3 ; 99. 3, 7; 113. 
20; 114. 3; 124. 27: 128. i; 
129. 6; 130. 23; 132. 16, 24; 
133. 8, 15; 134. 5; 145. 2; 
164. 16. 

TapcLTTCJ 104. 23; 153. 3. 

raats (‘ pitch *) passim. 

rarrcj 107. 23; 117. 9; 159. 15, 

TOVTOTrjS 105. 3. 
raxos 105. 12, 13; 124. 6. 
retj'o; 108. 4. 
rifCTotP 124. 25. 
t€A.€£os 99. 12; 101. 13. 

TcAcvTafos 111. 12 ; 129. lo; 146. 

T€Xos 95. 10; 129. 16; 130. I. 
ripvcj 97. 20; 138. 21; 144. 5. 

reraprrjfiopiov 117. 16. 

r€rpA.xop^ov passim, 
hib. TerTapojVy t6 (‘the Fourth’) 

TOfATI 138. 21. 


Toviaios passim. 

Toj'os(= (i) interval of a tone,’ 
( 2 ) ‘ key ’) passim. 

ToTTos (‘ compass,’ ‘ locus of vari¬ 
ation,’ ‘region or direction of 
the voice-series *) passim. 
Topvevrrjs 124. 25 . 

Tpls 141. 12 . 

Tpirrj (see Intr. A, § ii) 138. ii ; 
158. 20 . 

TpiTrj/Aopiov 117 . 5 . 
rpoiTos ( = (l) ‘ manner,*( 2 ) ‘ style 
of composition,’ ( 3 ) ‘ character ’ 
or ‘ motive ’) passim. 

Tpvirrjpa 132. 17 ; 133. 12 , 18 . 
Tpdirrjcris 128. 18 . 

Tviros 96. 16 ; 98. 5 ; 108. 1 ; 111. 
3 ; 119. 4- 

Tvnooj 97 . 21 . 

TVTTwdrjs 108. 9 . 

TvxdfVy 6 100 . 17 ; 110 . 9 . 

vyleia 122 . ll. 

inrarr) (see Intr. A, § ii) passim, 
vnaruiv (see Intr. A, § 29 ) 131. i. 
vir€pPcuvoj 102 . 3 . 
virepfiaros 109. 19 , 
vir€pPo\ai(uv (see Intr. A, § 29 ) 

131. I. 

{firepix^ 117. 5 ; 120. 25 ; 146. 

10 ; 148. 2 . 
inrepopia 134. 27 . 
vircpoxv 120. 24 ; 146; 147. 

vir€pT€ivaj 107. 7 . 
vircprikeios 112 . 14 . 
virodrjkocj 97. 20 . 

{firodwpios 128. 13 , 20 . 
viroKaTa<ppov4oj 122. 15 . 
virokrjif/is 122. 20 ; 131. I 2 , 18 ; 

132. 12 ; 133. 22 . 
viroarj/mivcj 119. 4 . 
viroTviroo) 110. I ; 143. 13 . 
viro<ppvyios 128. 17 , 20 . 
viroxatJ'a; 122 . 17 . 

(pavraoia 101. 24 ; 102. 8 ; 139. 11 . 
(pavkos 114. 20 . 

(pavkws 124. 24 ; 125. l. 
(pOiyyopai 102. 5 ; 103. ii; 106. 
23 ; 107. 12 . 

(pSoyyos (‘note’) passim. 


<ppvyios 128; 130. 13 , 14 . 

(pvcriKos 110 . 6 ; 119. 10 , 13 ; 128. 
24 . 

<pv<ris 97 . 21 , 22 ; 98. 3 ; 100 . 22 ; 
110. 2 ; 111. 10 , 22 ; 112. I, 3 ; 

113. 2 ; 119. 5 , 7 ; 120. 4 ; 125. 
24 ; 127 . 17 ; 130 . 25 ; 132. 14 ; 
133. 8 ; 134. 9 ; 135. 19 ; 143. 
I5> 23 . 

^vcw 97 . 20 ; 102. 23 ; 108. 18 ; 

114. 9 ; 120. 5 ; 123. 23 ; 132. 
19 . 

(see note on 96. 18 ) passim. 

XaAciros 106. 16 ; 108. 13 . 
X^ipovpyia 132. 7 , 18 ; 133. 17 , 
18 ; 134. 8 . 

Xop 5 i 7 104; 133. 13 , 16 . 

Xpaofjuu 95. II ; 110 . 16 ; 115. 5 ; 
124. 22 ; 139. 19 ; 142. 17 ; 
143. 12 ; 144. II. 

XpTitTipios 107. I; 108. 19 , 24 . 
XPV^^^ 112. 7; 129. 13 . 

X/J<5a (‘shade,* ‘subdivision of 
genus’; see note on 116. 4 ); 

115. 20 ; 126. 13 ; 138. 23 ; 
152. 22 ; 158. 15 , 19 ; 159. 12 ; 
160. I. 

Xpoyos 102. 3 ; 104. 6 ; 115. 8 . 
XA>w/xa (‘chromatic genus’) passim. 
XpcjpariKos (see Intr. A, § 6 ) 

Xa;/)a 160. 19 , 21 . 

Xo^pK^ 102 . 12 ; 110 . 4 ; 128. 20 ; 
150. 8 . 

XOttpKTfios 98. I. 

i//€vd^s 99. 20 . 

dxl>€\ioj 123. 10 , 12 .